They are required if you want to immigrate to the US [1], so I sure hope citizens-by-birth also have to follow similar rules. Maybe you don't need to prove anything because by default people would already either be vaccinated, or had to obtain an exemption?
There are vaccines required to attend public school, but if your parents just say "I refuse" they are not going to kick you out. These hard-core antivaxxers are pretty small in number though.