Is this good for becoming a prop trader?

Well, the only reason I'd be working is to pay for my classes and support myself.

 

join a prop firm that offers some training for remotes and go from there.

 

If you are really that good with C++, why don't you try to get into a more famous school like UCLA or USC instead of CSULB? Even though I don't necessarily believe in brand-name, sometimes it just makes things easier, especially when all the career ads emphasize "top tier" schools.