Indigo8
Having done a bit of light research, I have discovered that Elvis Presley recorded a song "High-heel Sneakers" which was released in 1964. As 'Sneakers' is the name still given to what are now called 'Trainers' in the UK, they must have been around then. Though, if my memory serves me right, they were called 'Sneakers' in the UK back then.
Incidentally I had a pair of 'Basketball Boots' back in the 1960s. They were made of canvas, had high tops, laces and had soft soles. I believe these are still around now and are usually made by 'Converse'.
Yes, I had sneakers. Just couldn't remember the name earlier. I probably wore them with jeans and a striped Breton top; that would be about 1963.
Before then teenagers tended to wear younger versions of what their mothers wore.