Let’s also remember that the American (continental) Western Coasts aren’t exactly prime spot for colonization: in North America, the Sierras, Rockies and Deserts...in South America, the Andes and Atacama.
On terms of geography, places as British Columbia, the US West Coast and Chile are quite isolated from the rest of the continent until our days...don’t imagine the Chinese (the Middle Kingdom) making too much of an effort in such distant and challenging coasts...
I think the North American West Coast is comparatively rich in resources as the Northeast for example.
However what if the Chinese discovered gold in California? In OTL thousands of poor Chinese peasants ventured out to California during the 1849 Gold Rush.
Could they? Sure, they had skilled sailors, a large surplus population, and the humble junk was a very seaworthy vessel.In terms of man-power and technology did anything aside from will, hold the Chinese back from emulating European post 15th century colonialism before the Europeans could do so themselves?
As for Africa, they could get Madagascar and the eastern coast. Indonesia and Oceania would be much better targets for a colonial naval China, and would also be helpful in colonizing Africa if that path was chosen, and so would be the initial Chinese colonies. The local Overseas Chinese communities in the area make it even easier. I also expect Indochina would be targeted, but I'm not sure how well that would go.
Eyeballing the map, I saw Oceania and Australia as the obvious targets in the medium term, with the Clipper Route making South America accessible from Australia in the longer term once Australian colonies are established enough to support expeditions of their own.
Very good point with a Chinese Australia using the Clipper route. Head east to South America through southern winds (the Roaring Forties, ideally), head west to home through the winds off Peru. Almost a perfect inverted mirror of the Spanish heading west through the Canaries to Caribbean route and then home through the winds off Florida. Chinese Chile and perhaps Patagonia would be very likely in that case, and Peru would be a key strategic objective.
If China makes a larger push into Manchuria, they might be able to make a cold Viking-esque journey to North America. This is one journey which would separate the boys from the men.
Why can't the Chinese use native slaves?On terms of resources yes, but much of such resources would only be useful by OTL late 18th Century, with the start of the Industrials Revolution...in an 14 or 15th colonization, fertile land is much more valuable and such spaces are severely limited at the West Coast
As of the Californian gold, could be an attraction but you need the 18-19th Century logistical tech to attract a major migration to the Americas...gold and silver were found by the Spanish and Portuguese by the 16 - 17th but migration was much more subtle, with major of the work performed by native or African slaves
Not saying that the Chinese would simply disregard the Americas, but colonization would be much slower and discreet than OTL (via the Atlantic shores)
If there was further technological and industrial growth under a surviving Song dynasty I could see it, though even then I don't think it would be inevitable. In Africa the Chinese would have the same problem with local diseases and resistance that the Europeans did, so they would probably stick to trading posts along the coast just like the Europeans did.
If the Mongol invasion is slower, I could imagine the Song from their last island and coastal holdouts sending expeditions Eastward in a desperate search for allies or refuge, and maybe even a Romantic final flight of the last Song Emperor to the New Lands in the East as the Mongol Hordes are burning Hainan to the ground. Unlikely but could make a cool story especially if the Ming send *Zheng He East to find out what happened to the lost colony...
It wasn't the Song, but there was a TL here where Tungning/Southern Ming flee to California due to the Qing. So that's technically colonising (a part of) the Americas before Europeans given that Spain had no real presence in California at the time.