The funny thing is that they were enslaved by the Babylonians. And they did wander through the desert back to their homeland once they were freed. A much bigger desert.
Because if it took them 40 years to cross the Sinai, something was seriously wrong.
So my guess is that at some point, some Hebrew King was like, “you know what? I like the Persians. They run Babylon now. And FUCK THOSE EGYPTIAN MOTHERFUCKERS! We’re changing the story!” And since the King was the voice of Yaweh on Earth, now they were freed from Egypt.