There are many variables to consider in order to answer your question. If the same weight category of aircraft does not require additional wake turbulence separation then it is as soon as the first aircraft is airborne the next can start take-off roll.
Then there is the standard 3 NM
RADAR separation with aircraft flying the same initial heading immediately after departure. The second airplane when both are similar types would have to wait until the first aircraft is about 1/2 NM
past the departure end of the runway (depending on the length of the runway) in order to establish 3 NM
separation when the second aircraft is RADAR identified.
Then the 15 degree divergence rule where the second airplane can start to roll just about immediately after the first is airborne if their courses diverge by at least 15 degrees.
Don't forget the use of visual separation either, that helps get things moving quicker at times also.
So many ways to keep airplanes moving at a controlled airport, just be creative if you're the local controller!
Any views shared are strictly my own and do not a represent those of any former employer.