American contemporary music settled into a slower tempo from 1960 to 1962. California "beach" music became popular. The break-out of new music was inevitable, but maybe not as sudden as it was when the Beatles "invaded" in early 1964. You had the Rolling Stones, the Kinks, the Dave Clark Five, so there was other British talent to fill the gaps in a wide-open American radio market.
Weren't Paul McCartney and George Harrison long time friends? Could they have formed a different band? Wasn't Paul the big Buddy Holly fan, so maybe his independent music would still be somewhat Beatle-like, even without John Lennon.