Based on George Do’s SEO walkthrough I’d say hitting a number one spot for a Google search definitely is possible if your product or service is niche enough. In the video, he shows an example of a smaller trekking pole retailer appearing above REI (a much, much larger retailer) in a search. So simply speaking, I think its totally possible if you’re lucky to have the proper keywords that your competitors lack. I think it is a matter of luck and timing, however, because larger retailers with deeper pockets have more resources to burn on other tactics such as advertising or even SEO consulting and may eventually regain the top spot soon enough. Especially if they find their competition (you) has gained an edge.
I think some websites may have it better than others, though. For example, if you are not selling trekking poles and are competing in a more tech-oriented market (say you are a retailer) even a niche product may be harder pull off a top spot on because assuredly competition in that market depends heavily on blogs with product rankings and forums for things like referral links. So, if it is common market practice to hunt for product descriptions in forums, larger retailers in that space may have already cornered in on those keywords and I imagine they spend painstaking amounts of time on SEO, especially if they are wholly online entities.
I do wonder though, how different the game is for services as opposed to goods because a unique service has a lot more potential of being niche than a material good.
TL;DR — It can happen, but perhaps not for long. Maintaining the top spot must be a constant effort.