Is there a viable path to a top Math PhD program through a non-flagship state school
It's too early to stress about grad schools in your situation. But let me share a few observations I have made being a student at a top 10 Math PhD program in the U.S


In every incoming class of last 3 years, there were a number of American students that came from a no-name schools such as a tiny liberal arts college nobody heard or a low ranked stated university. This means that if you are the best student in your university and make good friends with your professors, there is a decent chance to go to a much better school. I specified American students because international students pretty much all come from premier institutions. 
Do an REU in your sophomore or junior summer. The point of REU is not to prove something new, but to expose you to the research world. Ideally, impress your REU supervisor well enough to ask for a recommendation letter from him/her. 
Do not underestimate the Math GRE. Take your time to practice and get 800 minimum - 760 at the very least.