It'll be closer to 6-8 weeks since these early vaccines require two doses.
AFAIK nobody that got even a single dose ended up in the hospital. That's huge if true. That means hospitizations will plummet well before everyone is through their second dose.
Page 30 of https://www.fda.gov/media/144245/download
See this graph > Cumulative Incidence Curves for the First COVID-19 Occurrence After Dose 1, Dose 1 All-Available Efficacy Population
Also keep in mind this graph is probably based on COVID diagnosis date. Since it's unrealistic to test positive the day you contract COVID, I think it's reasonable to say it might even be effective from day 3-5 on
This is the most common question that I am asked at work.