Asian Growth Equity ($3B+) to U.S. VC

hello everyone,

I have an internship for the summer at a respected growth equity/VC firm in Asia with over $3B in AUM with a focus in tech. I go to a U.S. university/am from the U.S. and was wondering how I can take advantage of this opp. to transition to a VC firm in the U.S. for a full time position. Are there connections I can make maybe with firms we are co-investing with from the U.S. etc. or am I going to have to be on the ground sending hundreds of emails and calls again?

Background:
Junior at a non-target west coast school
previous experience working at a high growth tech startup with $300M in funding
Engineering degree