As metalinvader665 points out, you don't go due east from East Asia to get to America--you go northeast, along the coast, where the currents run and land is not far away. It just so happens that this curve is roughly a Great Circle--it takes one along the northeast coast of Siberia, past Kamchatka, to either the Aleutians or the Bering Sea, thence past Alaska to the British Columbia coast then on down past Washington, Oregon, and northern California until one stumbles on San Francisco Bay.
Getting home again is a whole different problem, compounded by the fact that west-bound currents go right past Hawaii across an expanse that comprises nearly a complete hemisphere of Earth! I daresay that ships that could make it all the way to say Puget Sound could manage to beat their way against the winds and currents back to Japan or Korea, but slowly and with difficulty.
And of course the intrepid East Asian mariner does not know that if they keep on trying, eventually they can find someplace as nice as Vancouver island to consider colonizing, let alone the California Central Valley or that civilizations such as the ones in Mexico lie beyond. Given current climatic conditions on Earth, what they are doing is sailing onward into increasingly bleak and storm-tossed waters, where the shores they might put in to are chilly and although apparently well-vegetated (except in the more extreme cases) rather poor in supplies. And yet withal inhabited, by suspicious natives who are more or less well adapted to their climates and ecosystems; these natives might be exploitable to a limited extent but are poor pickings, and yet able to inflict some serious hurt on unpleasant intruders.
Thus even if we transform the socio-political setting of East Asia by a whole lot, to make them more expansionist and venturesome, they are hardly encouraged to go that way. Some desperate persons just might, and even manage to fight their way back home to spread the word of more inviting lands (and perhaps even find some gold in various places to encourage more traffic). But sooner than go east by any route, they are much more likely to turn southward. Assuming that either they have already subdued Indochina, or been checked by indigenous civilizations there and seek to leapfrog past them, they will of course encounter the Philippines and the eastern arm of Indonesia first, and these will divert and absorb their efforts. If someone pushes on farther they find New Guinea which is tough terrain for temperate-adapted people to attack. Pressing on south (from what ports?) they do find Australia. Its northern shores are crocodile and snake infested swamps and behind these lie the arid Outback; neither are inviting to people from the Han Chinese core regions though perhaps south Chinese or colonists who grew up in the territory we call Vietnam might make a go of the wetlands, maybe. If they go east, they come upon the east coast, whose northern reaches are still very tropical--perhaps tempting to the tropical born among them--and if they keep on going south they find lands the Han find pleasant enough, though they are not used to Mediterranean climates.
The thing is, all this leapfrogging past the tropical belt to the north will surely divert and detain efforts coming out of China proper. If they are amazingly successful in dominating all of it, well, "China" is now a whole new giant thing, its demographic center of gravity shifting far to the south despite the possibility that population densities remain high along the Yellow and Yangtze rivers. Either the distant southern colonies and outposts, which must be somewhat culturally transformed by their very different climate, secede from distant homeland power centers and make a new belt of other nations and empires that aren't strictly speaking "Chinese" although they are very Sinicized, or the vast empire must move its capital southward, down into Indochina or perhaps beyond, and the original Han homeland plus the more recent southern belt become a set of peripheral far northern provinces, and any necessary cultural transformations will apply to the whole Empire. Very possibly now it is the northern homelands that secede, or as peripheral regions are abandoned to steppe conquerors.
So by the time the Australian east coast is within reach, very possibly the original Han people who might have been interested in settling it have a hostile tropical empire sitting between them and it, while the hotlands neo-Chinese have little interest in settling places like New South Wales or Tasmania.
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In an ASB context, where we envision WI the world were turned upside down, so China is in the Southern hemisphere, I pointed to the somewhat less severe, warmer and less stormy conditions apparently prevailing along the arc from Japan to Puget sound, and that places like Kamchatka, the Aleutians, and Alaska would be much more suitable for civilizations to develop, spreading from Manchuria and Korea and Japan on south. With more developed locals to trade with, trade networks could spread all the way to Puget sound and on to California and Mexico beyond.
We might get a similar result if sometime after the rise of civilizations, Earth warms up to the degree it did in the Interglacial previous to our own.
Even then though, China proper (moved inland a bit because of higher sea levels due to Greenland melting completely, and perhaps the Antarctic ice thinning a bit) would be a long long long way away from places like the California Inland Sea (flooding the central valley) and despite the lure of the gold on its shores, the people who interact with it and possibly conquer it would be more likely Alaskans or Puget Sound civs, which no doubt would enjoy some acceleration of civilization due to cultural imports from China (and nearer and relatively stronger than OTL Manchuria, northern Japan, Korea, and Kamchatka) including crops and draft animals--horses would probably run wild over North America again and this time perhaps be adopted as steeds by Plains Indians rather than all slaughtered for meat, and this would of course eventually transform Mesoamerica. Perhaps before any Pacific Northwest peoples get around to investing the California Inland Sea shores, the Mexicans would have extruded some branch civilization over land or coastwise to preempt them.
If in this long sequence of many thousands of years, China proper did undergo an aggressive and centrally directed expansionist phase, they'd probably be as preoccupied with Manchuria and Korea as I suggested with Vietnam and the Indonesian natives in the southward speculation, then have to work their way up the chain through Alaska, petty powers along the BC coast, and only then get a foothold in Puget Sound. California is still a long way beyond and Mexico and the Andean peoples, farther still. I'm guessing the Sinosphere proper would terminate somewhere between Alaska and Puget Sound, and beyond that would be mainly Native American civs much more developed, with draft animals and metallurgy. The West Coast natives would be partially exposed to the Eurasian pool of diseases over a period of thousands of years; they will still be terribly vulnerable if trade rises to level comparable to Early Modern Europeans in the Indian Ocean.
If we assume geography has something to do with China's persistent cultural characteristics, then even with higher sea levels and warmer climate there I see little reason it would be a lot different in such a warmer Earth scenario; their neighbors to the north seem far more likely to be the active agents of contact with North America; lacking China's deep demographic pockets and beginning contact many thousands of years before, they will be on a continuum with the American peoples and probably colonization in the sense of Europeans of OTL landing and sweeping native peoples off into a corner would never be possible; by the time the Han Chinese are showing up in galleon-junks or whatever, the Californians and Mexicans and Puget sound peoples would be nearly on a par with them; it might be possible to have domination of native civs in the manner 19th Century Europeans imposed on older empires and kingdoms in east Asia OTL, as China itself suffered in fact, but not founding some sort of New China on "virgin land." And more likely it would be Manchurians or Kamchatkans doing this domination, and putting pressure on the Chinese themselves!