[smabie]

Unless you do something really amazing, they will judge you on your school and grades. When you're older, it's different of course.

You can't really get any real trading experience unless you work as an instiutional trader, so no, you don't need to have traded.

You also don't need to know anything about finance, though it helps. With a math+CS degree from a top school, I wouldn't imagine you have trouble getting a S&T offer at a bank (maybe not a specific bank like Goldman tho).

The other path you could take is to go straight to the buy-side: prop shop, hedge fund, etc. These jobs are significantly harder to get.

The money won't be as good at the sellside, but it's a lot less risky. Also having a big bank on your resume never hurts. Probably the most common career path is:

summer bank internship -> 2 year analyst stint -> mba/mfe/PhD -> associate role at bank or buy-side fund