I have about 1350 total time, but I don't want to get stuck being a FO for a long time. Will they make you a captain once you get the minimums to be a captain?

I'm an FO at my company right now and it really sucks. Some people are kinda made to be FO's, but I am most definitely not. The problem is my company right now needs captains, but they arent going to upgrade me because its much easier to find a new street captain, rather than find someone to replace me as a FO. The street captains they're hiring have less time that I do right now.

I just don't want to get into another situation like this again.