There was one field scale test of the polio vaccine, in 1954. It included about ~700,000 children. There was not three years of staged testing, let alone millions of children within those three years.
There were 623,000 children in the field trial (placebo/non-placebo). There was an additional million who acted as controls (not directly a part of the study, but used a baseline measure of polio incidents in the population surrounding the subject).
While the entire study took over a year, different populations were "monitored" for, at best, six months, many less.
The trial size was massive, but its generally agreed to have been overkill.
The results didn't differ much from the first 150 kids they tried it on.
Please look up these timelines.