In Twilight, Jacob reveals that the Cullens are the same vampires who made a pact with his forebears many decades previously.
Yet the younger Cullens have only been attending school in Forks for a couple years.
Rosalie complains about the idea of having to move “again,” implying they’ve moved often in the past. The young Cullens have all been through high school many times, in many places.
How often did Carlisle move out of and back into Forks? In such a small town how is it he wasn’t remembered from previous stints of living there, even if decades prior? How could it be that only in La Push is his original visit remembered?
The expensive house (with metal screens that close over the windows at the push of a button) is the only indication of permanence in the town I recall other than the statement from Jacob. Everything else seems to fit better if they weren’t there at all, ever, before a few years ago.
Canon answers preferable (books only, not movies), but word of God acceptable.