I'm 20 and I have been a Research Intern at Cambridge, LSE, and Ashoka. While I began my research internships at 20 (when I had one independent research project), you can begin yours earlier!
Most students think that they need to have research experience or publications before applying to labs. However, you don't need to be an expert at research. My #1 advice to aspiring research interns/assistants is to not self-reject/self handicap.
So many students don’t apply to these positions as they think that they’re not “good enough”. The biggest hurdle to securing research positions is not a lack of research experience, it's the feeling of not being good enough.
Before you assume that you're not good enough, remind yourself that if you don't apply, you definitely won't get selected. But if you do apply, you might or might not get selected. What I mean to say is that you have better chances of getting selected if you apply!
Moreover, labs look for curiosity, dedication, motivation, willingness to learn, etc. much more than research publications or data analysis skills :D
James Clear sums it up in this tweet below