One of the major reasons why Spanish invasion of Americas was so successful was that Columbus voyages came just in the right time: Spanish had a huge standing army of war-toughened soldiers with nothing to do, nothing to lose, and eager for adventure.
Serendipitously, in the same year as Columbus discovered America, Spaniards drove Moors out of Iberian peninsula, and suddenly tens of thousands of tough warriors had nothing to do. The war has finished, and the soldiers found themselves with no skills except for war, no family, and no prospects.
And here comes Columbus with the promise of the pagans' lands with unheard of riches, waiting to be conquered by those who are tough enough and willing to take the risks. And the thousands of unemployed soldiers with nothing to lose and nobody to leave behind answered the call.
Apart from this coincidence mounting invasion of the remote continent across the barely discovered waters would be infeasible. It's not easy to find sufficiently many experienced relatively young soldiers willing to drop everything and go into the unknown.
For example, when British joined in they were far less successful, even though the route was more familiar by then: it was too expensive to mount an expedition from a relatively well-to-do society. Therefore the failure of the Roanoke colony. Even then, the first successful settlement by Pilgrims came in the wake of armed religious conflict in their homeland.
IMHO China, as well as most other nations at that time, didn't mount an invasion across the ocean because under normal circumstances the adventure would be prohibitively expensive.
People who have, so to speak, a comfortable middle-class lifestyle and a loving family are less willing to take considerable risks. This makes organizing a large scale expedition into unknown dangerous lands, with very little chance of ever coming back, prohibitively expensive in a thriving society.