There's no reason to believe native Americans/ First Nations weren't capable of falling large trees.
Sure, limb and sapling bows were probably way more common for the average joe for many reasons,
but nice bow staves were of high trade value then, just as it is with us.
I highly believe there were people who spent lots of time cutting and splitting staves for trade.
The First Nations in my area carved 10+man canoes out of one old growth cedar tree.
Would apparently take a team of guys over a week to fall one, but that's nothing compared to a 12" diam Osage tree.
Also, just because a tree is round doesn't mean all your staves will be crowned. I cut a 10" diam black locust, and a couple staves have backs flat as boards.