Starting a math degree: Roadmap for research?

To get straight to the point: I absolutely love pure mathematics, especially discrete mathematics. The problem solving process and how slowly, but surely one figures out a beautiful proof to an underlying lemma etc.

Now since I'll start my bachelor's degree this september, I was wondering how quickly I could get research experience? I understand my extreme limitations in understanding complex papers and such, but there is there no way for me to get my foot in the door in the world of pure maths research?

Author: JohnWickDaLegend