I have a job that starts pretty early. I often have to leave a few minutes before fajr starts. So if Fajr starts 6:10, I’m out 6:00.

To compensate I’ve been praying earlier, usually when I wake up. I was wondering if that is permissible?

by

No. This is wrong.
Praying before time is not right.
You have to re-make the prayers you prayed before time.