The thing with Maths is most of the things you will learn in your undergrad are around a hundred years old. So at least with pure maths, it is do cutting edge research before your final year when you have the foundation to start looking at that. However, there are some topics which are perhaps accessible with knowledge of first year math, but you still need to have the experience in coming up with your own conjectures and writing proofs. So the short answer is probably no for pure maths. But speak to your professors anyway, it doesn't hurt.

If you can program, you may have better luck with computational mathematics research. Perhaps you could help some people by writing code for the to implement certain algorithms or something for them. This is more doable without having understanding of the more intricate details. I've known final year undergrads who have made real contributions this way. Again, they had a who undergrad's worth of maths as their foundation.