Why did the Jews bake matzah when they left Egypt?
ותחזק מצרים על-העם למהר לשלחם מן-הארץ כי אמרו כלנו מתים: וישא העם את-בצקו טרם יחמץ משארתם צררת בשמלתם על-שכמם: ויאפו את-הבצק אשר הוציאו ממצרים עגת מצות כי לא חמץ כי גרשו ממצרים ולא יכלו להתמהמה וגם צדה לא עשו להם
The Egyptians were very forceful in sending out [the Jewish people] from the land, as they said: “We’re all going to die!” The nation took their dough before it became leaven; their kneading bowls were wrapped in their clothing, resting on their shoulders. And they baked the dough that they had taken out of Egypt into matzah, as it had not risen. This was because they were expelled from Egypt and didn’t have time to wait. They also didn’t bring any other provisions
The Torah tells us that the Jews were rushed out of Egypt. Their salvation came in a blink of an eye. Many of them were planning on baking food for their expected Exodus from Egypt. What seems to have been unexpected is just how willing and forceful the Egyptians would be. The verse tells us that when the Jews had to leave, their dough had not yet had time to rise. Indeed, Rashi explains that the Egyptians didn’t give the Jews a chance to let their dough rise. This would imply that if the Egyptians had been more patient, the Jews would have let their dough rise to be baked into bread. The problem with this implication is that it was the first day of Pesach! Bread is not only forbidden for consumption, but we are even forbidden from owning leavened dough on Pesach. How then could the Jews have intended to let their dough rise?
What further corroborates Rashi’s reading of the verse is what we say on Seder night. The Haggadah asks the question: Why do we eat matzah on Pesach? It answers that it’s in commemoration of the fact that the Jews didn’t have time to let their dough rise when they left Egypt. The Egyptians forced them out before that could occur. This is why we eat matzah. This again implies that the Jews would have allowed their dough to rise had the Egyptians let them. What could be the explanation? In fact, this question is addressed by many commentaries. Here are just a few suggestions.
The Ran suggests that the first Pesach didn’t operate the way we would have thought. Our Sages tell us that there were many differences between the first Pesach and the Pesach for all generations. For example, the Jews were commanded to eat their Pesach offering “in haste”. They were to have their loins girded, and their walking staff in hand. This was a special command for that time. In future years, when they still had the Pesach offering, there was no need to eat it in haste. We see then that that Pesach operated differently.
Another key difference we are taught is with the prohibition of consuming chametz, leavened bread. While Pesach for all generations prohibits consuming chametz for seven days, the Jews at that time were only prohibited the first day, the 15th of Nissan. We could say then that their intent was to allow their dough to rise, so that they could bake bread for the next day. The Egyptians didn’t give them the chance, so they made matzah instead.
This, however, isn’t enough to answer the question. There’s also a prohibition to own chametz during the seven days of Pesach. While it’s true they weren’t going to eat the bread on the 15th, simply owning it would be problematic! The Ran innovates that even though our Sages don’t mention his, we can suggest that the prohibition of owning chametz was also only for one day. As such, there was no problem for them to bake regular bread on Pesach, so they could eat it after the 15th .
Another approach gives a fascinating yet complicated interpretation of the verses. At the end of the parsha, the Torah records that Moshe commanded the people against consuming chametz. He then said that: “Today you are leaving Egypt…and you shall observe this service”. Rashi clarifies that the service being referred to is the Pesach offering. If that’s true, it must be referring to the Temple service of the offering, and not simply its consumption. Otherwise, the word “service” is inappropriate. If so, this statement was said on the 14th of Nissan, when they were offering the Pesach. How then could Moshe say: “Today you are leaving Egypt”? They didn’t leave Egypt until the 15th!
This approach suggests that even though normally in Jewish law, the day begins at night, we see in many places that this isn’t true with the Temple service. The first offering of the day is the one brought in the morning, as the morning is considered the start of the day. Since Moshe was discussing the Temple service of the Pesach offering, when he said “today”, he was considering the day beginning in the morning and ending at the end of the evening. Even though the Jews didn’t leave Egypt until the 15th in the morning, which even according to this opinion was a different day, the redemption already began the 15th at night. That was when they were given permission by Pharaoh to leave Egypt.
What this means then is that we have a new understanding of the opinion that the first Pesach in Egypt had only one day prohibiting chametz. Normally this is understood to mean they were prohibited on the 15th of Nissan, from that evening and the subsequent day. However, the whole source that the first Pesach only had one day of prohibition is the juxtaposition of the word “today” to the verse prohibiting chametz. Today implies only today was it prohibited, but not all seven days like a normal Pesach. Since the “today” of this verse is referring to the 14th of Nissan, and in that context, Moshe was considering that the day ends at night, that means the prohibition of eating chametz was only until that evening. The following morning, the 15th of Nissan, had no prohibition. That means that they were permitted to eat chametz, all the more so own it. They intended to bake and eat actual bread, had the Egyptians given them a chance.
There’s a similar but more expansive approach. Some say that before the Torah was given, the day was considered to start in the morning. It was only after the Torah was given to the Jews that the Jewish day is considered to start at night. As such, when the Jews were about to leave Egypt, their day was considered to start in the morning, and end at night. The opinion that says that the Jews were only prohibited at that time to consume chametz on the first day of Pesach, when did that day start? According to this understanding, it would be the morning before their Seder. Again, that means the subsequent morning would already be considered a new day. They would have had no problem then baking and eating bread.
Either way you understand it, we see from here an example of our Sage’s maxim ישועת השם כהרף עין, the salvation of Hashem can come in a blink of an eye. Even when things look their bleakest, we could find ourselves swept away to redemption. The Jews didn’t even have time to let their dough rise. Hashem couldn’t let them stay in Egypt one moment longer.
 Based on various sources which I collected
 Exodus 12:33,34,39
 Ad. loc.
 Haggadah Shel Pesach Maggid. Cf. Pesachim 10:5; ibid 116b. The latter only says we eat matzah because we were redeemed from Egypt, and cites v. 39. The Haggadah explains the intent of quoting this verse is to show that the hasty redemption from Egypt prevented the Jews from baking bread, and they were forced to bake matzah instead
 See the Ramban ad. loc., who reads the verses differently than Chazal. His reading is essentially that the Jews weren’t able to let the dough rise, due to the prohibition of owning chametz. The verse is stressing that the Egyptians forced them out, to explain that they didn’t have time to bake their matzah in their homes. They had to instead bake it on the way
 Ran to Pesachim 25b (in the pagination of the Rif) s.v. מצה
 Pesachim 9:5; ibid 96
 Exodus 12:11
 Pesachim 28b, 96b
 The Divrei Dovid by the Taz to Exodus 12:34 asks how could they be involved with chametz while its prohibited for when it won’t be prohibited. I suppose he means why wasn’t there a prohibition of handling chametz, when it’s likely to be consumed out of habit. Or he means how could they bake on Yom Tov for after Yom Tov. The Biurei Moharal ad. loc. by Rav Eliezer Halperin understood it to be the latter. He answers that nowhere does the Ran say that they’ll bake it on the 15th for the next day. He just says that they would have let the dough rise, so they could have it for bread the next day. The Ran could mean they would also bake it the next day
 The Tzlach to Pesachim 116b and s.v. כל שלא and the Divrei Dovid loc. cit. ask that since Chazal don’t mention this, it’s implicit that this difference doesn’t exist. If it did, they would have listed it along with the other differences
 The Mizrachi to Exodus loc. cit. suggests this is also Rashi’s opinion. It’s interesting that he doesn’t cite the Ran, considering he says the exact same idea
 Tzlach loc. cit.
 Exodus 13:3-5
 Ad. loc.
 See Chullin 83a
 See Berachos 9a with Rashi
 The Biurei Morahal loc. cit. asks that this understanding is untenable with Mechilta to Exodus 12:14, brought by Rashi ad. loc., which says that the “today” of when they left Egypt was the 15th in the morning. He provides an alternate understanding for how this could be reconciled with the Jews performing the Pesach offering service when Moshe said “today”. See there, where he also answers the Ran’s question by suggesting that the Jews weren’t yet told about the prohibition of owning chametz. They were only told about it after they had baked their dough into matzah. He says that the Rashbatz in his commentary on the Haggadah says the same. See also Divrei Dovid loc. cit., who says a somewhat similar explanation. He says that the Jews thought that the prohibition of owning chametz was only the first night of Pesach, like the הוה אמינא in Pesachim 96b. Hashem rushed the Jews out of Egypt, not giving them time to let their dough rise, in order to show them that the prohibition was also during the day
 This concept was first suggested by Rav Pinchas HaLevi Horowitz, known as the Hafla’ah. He applies this to non-Jews/bnei Noach even today, and the Jews before the Torah was given. He says this idea in his works Panim Yafos to Genesis 8:22 and HaMakneh to Kiddushin 37b s.v. בתוספות ד”ה ממחרת. He bases it off the verse ויום ולילה לא ישבתו (Genesis loc. cit.), which in the context of Noach and his sons mentions day first, and then night. The Hafla’ah uses this idea to answer a question posed by many Achronim: How could the Avos observe Shabbos if they had the status of bnei Noach, who are prohibited from observing Shabbos (See Minchas Asher Bereishis § 11)? He says that they observed Shabbos according to the Jewish day, which begins Friday evening and ends Saturday evening. Bnei Noach are prohibited from observing Shabbos only according to their day, which is from morning to evening. Since the Avos didn’t observe Shabbos on Saturday evening, they had no problem. See Binyan Tzion I § 126 who takes issue with this innovation. Teshuvos Bikkurei Ya’akov Orach Chaim § 4 by Rav Yaakov Chai Zrihen brings that Rav Shmuel Salant of Yerushalayim ruled like this Hafla’ah, in a case where a potential convert had a circumcision but hadn’t yet gone to the mikveh. This person wanted to observe Shabbos, and wanted to know if it was permissible. He was told to follow this Hafla’ah and observe Shabbos according to the Jewish day, but break Shabbos according to the non-Jewish day. The Bikkurei Ya’akov then brings many opinions who reject this Hafla’ah. See next note. See also Torah Sheleimah X-XI Miluim § 43 (p. 276 – 279), who feels he found a Rishon who holds like the Hafla’ah. As an aside, it would seem that according to the Hafla’ah, potential converts don’t need to purposefully break shabbos before their conversion. I subsequently found that this is indeed noted by Teshuvos Rabbi Akiva Eiger 1:121. It’s interesting that Rav Shmuel Salant seems to have only relied on it if the potential convert already had a circumcision, having begun the process
 The Bikkurei Ya’akov loc. cit. when listing those who agree with the Hafla’ah, notes it’s also the opinion of the Tzlach whom we discussed. He says the Tzlach uses the Hafla’ah to answer the question we started with. The problem is the Tzlach doesn’t say this. He only says the day starts in the morning with regard to the Temple service, which was the context of the derasha to prohibit chametz for only one day. The Bikkurei Ya’akov quotes his understanding of the Tzlach from the Teshuvos Toras Chesed Orach Chaim 25:8 by Rav Shneyer Zalman Friedkin. While it’s true the Toras Chesed does seem to compare the Tzlach to the Hafla’ah, and he writes that the Tzlach says דאז היה הלילה הולך אחר היום, implying like the Hafla’ah, the Tzlach as we have it doesn’t say this
 This idea is expressed this way in Midrash Lekach Tov to Esther 4:17. It appears in a similar fashion in Mechilta to Exodus 12:42 (brought by Rashi to v. 41) and Midrash Tanchuma Bo § 9: כיון שהגיע הקץ לא עכבן המקום כהרף עין