Actually the pill and JFK’s 1965 Immigration Act came at about the same time, the flood of the world into our nation was legislated to defeat the American voters, not to compensate for some disappearing population.
Yes, it started earlier, but immigration initially was a small amount. Kennedy swore that it wouldn’t be used to upset the racial balance of the country despite the quotas set-they were all from third world countries. Without border control the flood was even worse. All of it intentional of course.