Forgive this advisor, but I am shaking my head. It would seem rather presumptuous to assume a future PI with a way future possible presentation would know you well enough during this cycle to have a strong LOR/LOE for you this cycle. If you try to get a letter too early, it will be light on "evidence" (ie length of time knowing applicant) to have much impact. If you do later in the cycle, your file may be held open for the letter to arrive before being considered complete and on for review. This is the proverbial position between a rock and a hard place.
So first the bad news/advice:
If you feel that this letter, position, and presentation are so vitally important to you, then you may want to consider skipping this cycle.
Now the good news/advice:
Most applicant overestimate the weight of PI/Research Letters on the impact to adcoms.
In a 2013 AAMC survey* where 127 medical admissions offices responded,
found research experience is only of medium importance at private schools and of low importance to public schools as an experiential factor in offering both interview invitations and acceptance. Healthcare experience, community service/volunteer experience, experience with underserved populations, navigated through cultural barriers or challenges, leadership experience were considered of higher importance in factors for interview invites and offers of acceptances
*
https://www.aamc.org/download/434596/data/usingmcatdata2016.pdf
see page 3 (pdf p7) Table 1. Mean Importance Ratings of Academic, Experiential, and Demographic Application Data Used by Admissions Committees for Making Decisions about Which Applicants to Receive an Interview Invitation and Offer Acceptance (N=127)