We had a thread on that a while ago, and I did a bunch of research at the time. Here’s what i posted.
Unfortunately, the NEJM has moved the graphs so they no longer show up nicely in the thread, but you can still see them if you open the article.
TL;DR you get almost no immunity right away. You develop a lot of immunity about two weeks after the first jab, and the additional benefit of the second jab is mostly accrued within a week.