Pesach

What does the Haggada mean "The reason for Matza is because the dough of our fathers didn't even have time to rise before Hashem redeemed them as it says (Shemos 12,39) "They baked the dough which they brought out of Egypt into unleavened bread, for it had not been leavened, for they had been driven out of Egypt and couldn't delay...""? They couldn't have let the bread rise even if they did have time! Pesachim 96b- They weren't allowed to have Chametz that year just on the 15th of Nissan. Shemos 12,39 is talking about the 15th of Nissan! Therefore they couldn't have let the bread rise that day even if they had as much time as they wanted, so what's it mean the only reason they didn't let it rise is because they didn't have time?

(See also Pesachim 21b which makes it clear that the passuk that Pesachim 91b learns that they couldn't have chametz on the 15th from, isn't just talking about eating.)