Did Moses live at the same time as Noah?

No. Moses lived in the period around 1400 BCE. That is an
approximation, and scholars will debate the exact date. Some would place
the Exodus from Egypt (under Moses) as late as about 1300 BCE, others
would date it at around 1460 BC. That is a fairly wide time frame, but in
any case, it is very long after the time of Noah.

It is very difficult to say when Noah lived. Genesis chapters
seven and eight, which is where the story of the flood is found in the
Bible goes back to a time at which it is very difficult to put a solid
date. Some have tried to use the genealogies recorded in Genesis to try
to date the flood of Noah, but there are a number of problems with this.
Jewish genealogies often skipped one or even multiple generations. We can
see this even from the specific examples recorded in the Bible. The
phrase “the father of” in Genesis can be used to mean the ancestor of. A
specific example of biblical generation-skipping is found in 1 Chronicles
1:24 which fails to mention Cainan, the son of Arphaxad (Luke 3:36).

Bottom line, Noah lived over a thousand years and perhaps
thousands of years before Moses.

John Oakes