This is like saying that you will never buy a new car because you don't have years of data to prove the car was built correct and is safe.
There is a risk that a new car has a problem that only shows up after 20k miles, but the people who approved the new car have a lot of experience approving cars and a track record of not missing major safety issues.
Good car analogy. Though it slightly breaks down in that some cars have turned out to have problems (hence lemon laws), whereas as far as I know no vaccines have ever had any bad long term side effects.
There is a risk that a new car has a problem that only shows up after 20k miles, but the people who approved the new car have a lot of experience approving cars and a track record of not missing major safety issues.