According to traditional chronology, the Exodus was in 1312 BCE. Non-traditional chronology places it earlier. However, it does not state explicitly that the route of the Exodus involved crossing the Nile. See also:
If they followed Moses, then yes they did.
The mother of Moses put him in a basket, and out him in the river Nile.
Moses did not 'found' the River Nile. Nor did he find it.
The river Nile
Moses was rescued from the river Nile, by the Pharaohs daughter.
Moses was found in the river Nile.(Exodus 2:2-5)
Moses sister was called Miriam, her job was to watch over her younger brother Moses in the basket, in the Nile.
It was the river Nile.(Exodus 2:3-6)
The Nile River
the basket in the Nile
The Nile.
Moses