They didn't manage the land and its resources. They lived a nomadic lifestyle. Once they'd depleted an area of its resources, they simply picked up everything and moved somewhere else.
Who told you that? Because they lied to you. First, there was substantial variation in lifestyle. Second, they didn't just deplete an area and then move. They practiced land management, and they had the land portioned up into different groups' territories. In the west, they lived in relative stasis, and in the same places, for over ten thousand years. They successfully managed forests (with yearly controlled burns), oyster beds (by not overcollecting from them) and fish stocks (by not overfishing.) Their yearly burns kept the oaks and redwoods healthy, by clearing the understory. The oaks provided more food than they could eat every year. Then whitey arrived, in the form of Andrew Kelsey, who enslaved, raped, and murdered the locals. Some of them understandably got upset and killed him. Then we sent the US 1st Cavalry up here to murder all the Pomo on Bo-no-po-ti, aka "Island Village". Literally only one girl survived, hiding in the reeds while the lake went red with blood. Later, the federal government paid the locals $1/tree to plant black walnuts, as motivation to chop down the oaks upon which the natives depended for food, oaks in healthy forests that they had maintained literally for millenia. The walnuts were never financially beneficial to the area, and few remain today.
In the Midwest, the natives deliberately burned forests to create more range land for the bison. The bison then maintained the land in a state suitable for their use, which left the bison suitable for the use of the natives. The natives would follow the bison herds, since that was their primary source of all things.
Sorry, I'm not familiar with the natives of the East.
Now, to be fair, if you go down and check out the natives of Mexico, they were eating one another, and they deforested the shit out of their land and they ran out of food and they migrated or they died. But up here in North America, the natives most certainly did practice sustainable land management.
Europeans arrived with a much higher population density. They would've had the same detrimental effect on the North American environment even if they'd lived as the native Americans did.
We'll never know, because they didn't even try. They did the opposite. They deliberately destroyed the lifestyle of the natives. They killed all the bison, a free renewable resource, so that they could carve the land up into fenced portions that someday, nobody would want to live on anyway. Seriously, do you think they would have killed the bison if they knew that someday all that territory would be known as "the flyover states", just a bunch of shitholes with poor civil rights? And they deforested the shit out of the west so that they could run cattle here! All they had to do to have more cattle than we could use was not kill all the bison at once.