The Pilgrims were in pretty desperate shape when they got here, and they quickly recognized that they needed to work with the Native Americans. They didn't start stealing land and everything that resulted in until the next generation, which was full of people who's lives weren't saved by the Native Americans.

Other settlements had been fighting the Native Americans for a while, but they're not who Thanksgiving celebrates.

Also, they were trying to get the Native Americans to leave. It can't really be called a genocide until America was large enough that there was nowhere to leave to.