Difficult cold start

Today I took off air filter and sprayed a little amount start pilot to carburetor (throttle open).
Engine started immediately.
I don't know if this proves anything but I think there could be something wrong with carb, but what it would be?
Accelerator pump gives strong squirts. But if engine should start without pumping gas, I don't know if that pump is needed to start cold engine at all, if everything is ok?