While some occurrences of “seven” are incidental, others are intentional, such as what the Lord told Israel about the Feast of Unleavened Bread,
“You shall keep the Feast of Unleavened Bread (you shall eat unleavened bread seven days, as I commanded you, at the time appointed in the month of Abib, for in it you came out of Egypt; none shall appear before Me empty)” (Exodus 23.15).
They had to leave Egypt the moment Pharaoh gave the order, which meant that the Israelites could not wait for their bread to rise, but they would have to take the dough without leaven, and be on the run for a while.
The seven days of unleavened bread would remind later generations what their forefathers had to go through to escape Egypt, and what they had to go through to enable those later generations to be able to live in their own land, the Land of Canaan.
Therefore, the seven days of eating unleavened bread reminded them of the work of God, and seven days was sufficient to create this reminder.