Engineering

Yeah, you can 😄

You can do M.Tech without GATE at many private universities. Thapar University, for example, allows non-GATE candidates through its own selection process (based on academics, sometimes a test/interview).

That said, GATE is needed if you want top government institutes (IITs, NITs) or a stipend.
No GATE = private universities like Thapar, VIT, SRM, etc.

So yes — totally possible, just depends on where you want to study.