Is it possible that nearly human mammals existed before the last mass extinction dinosaurs?
The ancestor of all mammals lived about ~180 millions years ago (see here), so much before the Cretaceous–Paleogene extinction event (~65 millions years ago). The ancestor of all primates lived ~65 millions years ago (see here), so pretty much at the same time as the C-P extinction.
But please, don't picture the ancestor of all primates as something that is too human like. It looked more like a lemur, a tarsier or a loris, than like a human!
The first great ape lived about 14 millions years ago (see here) and the most recent ancestor of chimpanzee, bonobos and humans lived about 6 millions years ago (see here). The discovery of how to control fire happened about 1.5 millions years ago (with a pretty wide confidence interval, see the wikipedia article). The first generally considered Homo sapiens lived about 200,000 years ago (see the wikipedia article). The wheel was first invented about 5'000 years ago (see the wikipedia article).
Related: Who are humans' closest relatives, after primates?