Possibility for clearance after starting on a non clearance project

I’m a new hire set to start on a project that I believe does not give me security clearance. I honestly don’t even really want to work on this client and was just planning on trying to move projects in a year or so but now I feel like I’m going to be stuck on this project because I didn’t get the opportunity to get clearance. Is it possible and is it likely that I’ll be able to find a different project at some point over the next year that will sponsor my clearance?