I find it highly likely that crucial bronze age inventions like smelting, Eridu/Elamite 'pyramids' and writing were introduced to America in one way trips between 4000 and 0BC, however until we find artifacts or mummy DNA it's pure speculation.
Civilizations around the world definitely acquired similar technology with suspicious timing, but the common factor doesn't need to be humans. One theory I'm fond of is river deltas. The major ones all formed around 7,000 years ago (see https://www.youtube.com/watch?v=A47ythEcz74) as a geological result of the end of the ice age. After humanity spread to the Americas during the ice age, the end of the ice age seems to have created the conditions necessary for agriculture to flourish. Once you have agriculture you get cities, writing to track harvest numbers, pyramids from laborers working in the off season, and metalworking from craftspeople .
Suspicious timing is a good term. As far as I know the 4000 years of development which preceded the Eurasian bronze age are absent in america (tokens, cold hammering, accounting, step by step increases in architectural complexity), even though agriculture must have been part of a much earlier package or human condition as you said. Wooden idols and totems go back to ice age times, I give you that.
I don't doubt there were "rafting" events, like that which brought over the new world monkeys, but I don't think isolated individuals can transmit culture like that.
"Connecticut Yankee" type stories underestimate how diffuse culture is, and overestimate the prevelence and prowess of "polymaths" in the weakest sense.
Rafting is not the term I'd use for post Ubaid sailing and rowing explorations. Look at the rock art of that time, especially in egypt and slightly later scandinavia. If you believe the essence of Gilgamesh, some of these expeditions to far countries might have even made it back (though unlikely from America).
