Im not 100% sure if it’s brass. to be honest I have zero idea on the case material.

I want to make it shine again. is there a way to polish/restore this type of case?

 

It’s plated so no. The Chrome or Nickel plate that remains might shine up but be careful, plating is very thin and the oxidation is happening under the plating where the base metal is exposed. Is it a Zenith case?

 

Please show the underside of the case. The first indication that a case is plated is usually where the underside of the case lugs contacts the wrist. That is usually the first place for the plating to corrode through. There is a chance the case is just filthy, and with a good soap and water wash and ultrasonic cleaning, it may be enough of an improvement without polishing it. By the way, such an intensive cleaning should be done with the mechanism OUT of the case. And plan on replacing the crystal and gasket (if there is one).