Advice sought on joining US based PE and VC firms

Hi,

I am a final year undergraduate student from Europe, who are seeking advice on joining US-based PEs and VCs. Even though I'm an undergraduate student, I have already received interest from European PEs and VCs on joining them after the end of my studies. This is probably due to the fact that I have already for more than a year worked part-time with McKinsey as a consultant and studied a semester at Harvard University. However, my dream has always been to work within PE or VC in the United States, and therefore I would like to know if that would be possible considering the current stage I am in? And if yes, how should I do it?

Thanks in advance