A great many women who had children from 1955-1964 wanted exactly two children, but due to contraceptive inefficacy compared to the Pill, they ended up with 3+. And women who wanted large families of 6+ found themselves having around 5-6 with a suspiciously high frequency.
Long story short, even without the Pill, the desire for contracepting into a smaller family was already baked into the postwar cake for American women. It’s not clear that large family desire is particularly common to American women when they aren’t part of an intensely religious subculture. Frontier women had large family sizes, but this is confounded by the frontier being a hotbed of highly religious subcultures.
Now the story of how more education for women went from being strongly correlated with fewer kids to…not is a different story, mostly still unwritten by any demographic researcher.