it should be able to run right after starting unless it's Really cold outside like freezing or below. Mine starts, then I turn the choke off after about 5 seconds and it revs after about 15 seconds and that's at 40 degrees F here on a cold morning.
I won't ride it that cold without letting it warm up for at least 3 to 5 minutes, but it should be able to rev without stalling somewhere between 15 and 30 seconds after a cold start.
Check for vacuum leaks at the carb, manifold, and the base and cast gasket, you can use carb cleaner or propane to check for leaks as the engine will rev up a little when you get the propane or carb cleaner close to a leak.
Crank seals are notorious for air leaks when it's really cold too and those leaks will tend to seal up as the engine warms up, making them difficult to find in some cases.