What's your definition of "immigrant into the USA" here?
You aren't required to get immunized for H1B and a number of other visas, but for green card (aka permanent resident card), you are absolutely required to get a general medical exam + screen for TB + get up to date on all your vaccinations. You need to do it shortly before the green card interview, because you are expected to bring those papers with you for the interview.
https://www.uscis.gov/tools/designated-civil-surgeons/vaccin...