Was Moses "Jewish"?

If Moses was of the tribe of Levi from both parents Exodus 2:1-3, and he never lived in Judah/Judea, in what way was he a Jew/Judean G2453 or "Jewish"? I have an understanding based on crystal clear scripture, and I've been told it's a false interpretation, so I am here looking for actual experts who can offer sound scholarship. Any takers?