Top 20 what - for CS, what you think is top 20 isn’t top 20.
My nephew works at one of the biggies and has a degree in Poli Sci from Arizona. It’s his second biggie -his old boss just recruited him to a bigger company.
You can be successful in poli sci from anywhere - and many will require a competency test to hire you (how he got in with a poli sci major) from a state school.
Would a top 20 or Ivy be feasible - and I’m using the US News list, not a top CS schoo? A reach - but possible if you apply but doubtful.
Would a UMD or UMN or RPI get you a similar or even better outcome? Quite possibly.
Good luck.