It's pretty easy to see that there has to be a contact patch of some size. Imagine two balls coming at each other at the same speed. There's a plane between them that neither ball will cross. Because the contact is not instantaneous, there must be a round flat spot (or nearly flat) of the contact between the balls.
If you know the size of the contact patch between the balls, you can fairly easily calculate the contact time if you know the speeds of the balls. Or you can measure the contact time directly, as Dr. Wayland Marlow showed in his book on billiard physics. That time is about 100 to 200 microseconds depending on the speed of the shot.