I have an ongoing problem with a new vessel sink.
Question is there a minimum length between the bottom of the sink and the P-Trap?

Vessel sinks hae a very bad problem about draining slow. It is the way the plumbing is installed. It has no way to get air so it can "Breath"... to test if this is the problem you can get a soda straw, put lots of water in the lavatory, let it start draining and if it is slow stick the soda straw down into the drain but leave the top of the straw above the water level. If the water drains faster then this is the problem. If now it could be a clog in the drain.

I have an ongoing problem with a new vessel sink.
Question is there a minimum length between the bottom of the sink and the P-Trap?

To answer your question, no there isn't. Why do you ask? Regards, Tom