If your domain is new, and Google hasn't found your site you'll probably be sandboxed for a few months (penalised so lower listings). You can get around this but I'm not telling If however you are in a non-competitive area you will likey get listed pretty quick but you'll still be pages down.

Your domain containing your product help a great deal.

I'm constantly running 'experiments' to check out how the search engines are handling things, don't believe most of the crap you read elsewhere.