(Depressing, I know)
Inspired by a particularly weird game of Victoria 2, but would deforesting and colonizing the Amazon have been within 19th century capabilities?
Short answer. No.
Long answer. No, Europeans would have problems with the tropical environment especially diseases, so you couldn't get enough whites to do it. Nor could you enslave enough locals to do it. Why would anyone be willing to destroy their homes for mad whitemen, when they can just slip into the jungle and find a new home. Besides, what would they do with the deforested Amazon, even if they managed it, somehow? the land would lose fertility in a couple of years, and they'd create a desert.
Long before you got very far into the basin, it would be obvious that it was a futile exercise, and they'd give up.