Anything is possible with enough patience and time.
Most people I know started out small and had to build up their collections over years. Unless you are already pretty well off, it will take time to get high dollar games...much less, several.
Look for deals. Browse ads numerous times a day. Put ads out that you are looking for pins. Fix up and sell what you can. Tell all your friends, family, and co-workers you are looking for pins (you never know where they will turn up). Offer to trade other non-pin things.
Btw: what is your dream pin?