Basically, the Beatles and Rolling Stones did not create youth culture. They were, though, key components of its sound.
The early sixties were a time when the overall tempo of popular music in the US would slow down for a couple of years. The cutting edge of rock and roll would divide itself between Detroit and London, with neither side quite aware of the relative significance of their work.
The fall of 1963 was the first year that all levels of grade school and high school were filled with children of the Baby Boom. A youth culture had emerged in the fifties with Elvis, Buddy Holly, James Dean and the beatniks. It was ready to take center stage in the sixties with the influx of the emerging generation.
For the Beatles not to invade America, we must assume the group never formed. The same for the Rolling Stones. Now, there were too many other artists to completely prevent an influx of British music. You still have the Dave Clark Five, the Who and the Kinks, to name a few. I would expect a gradual influx and mixing of British rock with American Soul. Keep in mind the American civil rights movement is brewing at the same time.
There would be a Jimi Hendrix, a Bob Dylan and The Doors. They just might not sound exactly the same as we remember. The youth counterculture movement would still emerge in the mid and late sixties; whether they would still be called "hippies" is anybody's guess. Even without the Beatles, long hair might still emerge as a protest to the war and military dress codes. We must remember that the number of people who participated directly in the hippie movement was very small compared to the number who emulated portions of its music and style.
What about punk rock? By the time you get to the seventies, rock music will have evolved. As for the punk trend, who knows. When you take away major contributors like the Beatles and the Rolling Stones, you are going to change the sound of contemporary music for decades to come.