Yup, AVB has nailed it, I'd say.
Sounds very much like a priming issue, and the most common cause of this on these Quantum engines, is a warped air filter base.
The primer bulb pressurises the carby float chamber, so as to push a shot of fuel through the main jet into the venturi.
If the air filter base to carby joint leaks around the primer gallery, it won't prime.
I have a Quantum XTS50 on a Masport, and it's a 'first pull after 3 primes' start, from cold. Easily the easiest starting Briggs I've owned.
