Starting an engine from cold requires a richer (more fuel, less air) mixture than the engine needs when it’s up to operating temperature. Because the inside of the engine is cold on the first start of each day, this richer mixture gives the engine the chance to run smoothly and not stall. Remember old cars with choke levers? It’s the same thing except that now, the computer controls the choke.
So, yes, that’s why you sometimes detect a petrol smell when a car first starts up. But make sure the smell goes away and doesn’t stick around the whole time the car is running, or you could be looking at a fuel-injection problem that will need addressing. And don’t confuse a petrol smell with an oil smell. If you can smell oil or see blue smoke on start-up, then you’re possibly looking at a worn or leaking engine.