Should I clean a new airbrush before using?

I Dunno!

     This is fact. Every time I buy something like a New Airbrush, I do run it through a cleaning cycle, that way if it gets cantankerous I know it's not from the way it was assenbled at the factory and all their dust is off of it!

Neat thing about spraying with thinner is that thinner is easiest thing to spray.  Thus it becomes a test,  If it doesn't spray thinner there is a problem.

It can't hurt.

I also shoot a little thinner before each time I use just to make sure it's not blocked,before I add paint

You can have some machining residue in a new airbrush. I usually just pull the tip and needle. Flush those and wipe down. Then squirt straight through the body with a squeeze bottle of lacquer thinner or sometimes Iwata Medea airbrush cleaner. Minimally invasive routine and put it back together. I follow that with spraying either alcohol or lacquer thinner through the brush and check the pattern. All that takes about 5 min. lol. Now I consider it ready for paint.

I remember one guy here in the forum upon removing the head and nozzle tip on a new AB, found metal shavings inside. So you don't want to risk shooting that stuff forward into the tip. But even if that's not the case, there can be machining oils and such.

I always give mine a thorough cleaning when new.  Take off any residues that may not play nicely with paint.