Not before the current official terms have been verified and the applicant has checked LPR eligibility, admissibility, visa availability and the supporting documents USCIS requests. Liquidating first creates a tax event for a process whose terms may change.
Verify, then liquidate, then pay
Hypothetical example: a Quispamsis executive's shares vest in tranches and he wants to sell a tranche early to have the funds available. The protective sequence is to check the official program page and FAQ on the day of decision, confirm lawful-permanent-resident eligibility, admissibility and visa availability, review the supporting documents USCIS requests with Form I-140G, agree any corporate sponsorship terms in writing and only then arrange the sale and payments in the official order. Executive Order 14351 gives the gift an evidentiary role under specified EB-1 and EB-2 grounds, so an ordinary career-criteria screen should not be substituted for the official process.
Selling first locks in a tax consequence for terms that may change. Any visitor trip or a spouse's TN application remains separate from the Gold Card timeline.