My wife was here nearly 3 years on a valid VR by extending every 6 months, I believe
@WeegieInOttawa will tell you the same thing. So it's entirely possible to enter for 6 months initially then keep extending to go for common law and then extending further to stay here during the process. It's fairly easy for Americans and anyone from visa exempt countries to do this once in the country, obviously I wouldnt turn up at the border and tell the agent your plans, just say coming to visit your girlfriend for a few months, best to have a return ticket booked at that stage (obviously cant if driving) and only come with 1 or 2 suitcases and some funds.
When it's time to extend after 6 months I would just say wants to spend more time with girlfriend blah blah, if you're going for common law you will need to make sure you build up some proofs of living together, and shared expenses etc, Then get your PR app ready to go right after the 12 months mark has elapsed, when it's time to extend beyond 12 months then you could pay for the PR app upfront and include the receipt with the Visitor extension app as proof of your intention to apply for PR.