Well, I would say that fragile, short time when the colonists and Native Americans actually lived together peaceably for the most part. There were go-betweens from the Europeans and Native Americans who met together and made treaties to try to live in harmony.
In Pennsylvania one reason there isn't a huge Native American population today is because many of them ended up intermarrying with the colonists as a result of the general peace between them. Some also did move west (long before the Trail of Tears happened) and of course there were kidnappings and massacres and conflicts between them and the settlers eventually.
But for a short time in the 1730's, there was a time of relative peace between them and the settlers. Treaties were respected and land was only bought legally. It was the French and Indian War that really destroyed this relationship - when the French convinced some tribes to side with them against other tribes who had sided with the British. Relationships were never the same after that, and not surprisingly treaties were subsequently ignored and conflicts got worse until (in Pennsylvania at least) there were no longer any full-blooded Native Americans in the state.