Given that
Zheng He's fleet had ships a dozen times the size of the Santa Maria, I'm quite certain the Chinese would have the capability to build large ships by the time the Honorable Chairman takes power.

Chinese colonies are more difficult, as they lack a reason to go. Why bother sending fleets 5,000 miles across open water? The best a China-Colony-fan can hope for is Chinese Australia.
I'm not disagreeing with you, but let me expand a little.
Presuming that some Emperor or dynasty gets a serious yearning for exploration (I'm not going to speculate on cultural changes that would be necessary for this to really happen) . . .
The Chinese know where India is, and where the Phillipines are, and Indonesia as well. So that's the logical starting point. They keep sailing to the next island over, based on reports from merchants.
I can see Chinese fleets sailing from island to island in Polynesia, where the inhabitants of one island tell them, "Yes, the next island is over the horizon, about this far away and in that direction". So they could end up in Australia or New Zealand no problem. What I don't see is them making the jump to Hawaii, and if they did, why would they go from Hawaii to North America?
Few people in their right mind get in a ship and head "out there" in an indeterminate direction with no indication that there is anything out there to find. Most of the European explorers were looking for something that they had some evidence was there.
For the Chinese to find North America, they would have to sail north, past Korea and Japan, up to Siberia, and then decide to keep exploring that icy hell further and further east until they get to some place where they would be willing to settle.
Or you'd have to posit a burning desire to get to Europe bypassing something bad in Central Asia (Timurids? Worse?) and with the same crummy mathematics and ability to sound convincing that made Columbus convince someone you could get to the Indies sailing west before you ran out of supplies (wouldn't have happened even if the Americas weren't in the way). Part of the problem is that the 'get rich by bypassing the Ottomans and Italians' motive doesn't exist for China, because they don't go somewhere to buy luxury goods to bring back to target markets, instead foreigners go there to buy luxury goods. Essentially, they were too rich and comfortable economically speaking to really want to explore.