Multiple lines of evidence show this prediction came true in the intended sense (national supply and eligibility, not that every willing person actually did get vaccinated by that date):

• On April 30, 2021, White House COVID coordinator Jeff Zients stated that the U.S. had just shipped its 300 millionth COVID‑19 vaccine dose to states, tribes, territories and federal channels, and reiterated that by the end of May the U.S. would have enough vaccine supply for every adult American. (bidenwhitehouse.archives.gov)
• A CDC‑based cost analysis shows that about 284.6 million doses had been distributed to jurisdictions and 284.2 million administered by May 31, 2021, not counting some federal channels, which is consistent with a total national supply above 300 million doses when federal programs are included. (pmc.ncbi.nlm.nih.gov)
• By April 19, all U.S. states had opened eligibility to everyone aged 16 and older, meaning that by the end of May, any 16+ American who wanted a vaccine could at least book and receive doses as supply allowed. (en.wikipedia.org)
• Independent analyses at the time (e.g., McKinsey) projected that manufacturers were on track to supply enough doses for all eligible U.S. adults by the end of May 2021, and contemporaneous surveys from KFF showed the main emerging constraint was demand, not supply. (mckinsey.com)
• News coverage in early May reported states beginning to turn down federal vaccine allocations because local demand had slackened, further indicating that vaccine supply was no longer the binding constraint for adults who wanted shots. (en.as.com)

Taken together, these data show that by the end of May 2021 the U.S. had shipped on the order of 300 million doses and had broad 16+ eligibility with excess supply, matching Sacks’s prediction that there would be sufficient vaccine (around 300 million doses) for every American over 16 who wanted one to be able to receive it by then.