Dear 100 Hour Board,
Why did God wait 400 years to free the Israelite
The LDS Old Testament Manual gives several reasons for that long wait. First, God needed Israel to grow to fulfill His promises to Abraham. The original family, consisting of only 70 people, wasn't nearly large enough. In addition, Egypt was relatively wealthy and conflict-free compared to the rest of the region, allowing the Israelites to quickly grow. Next, having a common enemy created a sense of unity among the Israelites. This had the added benefit of Israelites remaining separate and not intermarrying with the Egyptians, allowing for a "pure race."
The story of the Israelites' escape is also commonly cited by many prophets to illustrate how God will always deliver His people. While I'm certain God didn't wait just for a good story, I wouldn't rule that out as one of His reasons.
-guppy of doom