I think there is a somewhat confused view, voiced by those who seem to perceive the loss of technological and economic supremacy that china enjoyed up to the 1400s to be attributable to European risk taking in colonizing America, that suggest china should now seize the new chance and grab the moon first and thus perhaps fix the course of human development in Chinese favor for the next few hundred, or even thousands of years.
This is an entirely fallacious view. The moon is not comparable to the islands in the Caribbean which the Spanish first reached in their quest to conquer the Americas. The moon is more comparable to Greenland.
The colonization of Greenland didn't make the colonization of any other parts of America easier, just like these is no reason in physics or chemistry why colonizing the moon will make colonizing any other part of the solar system any easier.
The colonization of Caribbean islands, on the other hands, did make Spanish inroad into central and South America easier, in a way the colonization of the moon will not do for colonization of Mars.
Finally, the colonization of America was possible because the colonization first occurred where payback was rapid. Spanish colonization more than paid for itself several times over within 30 years. Within 60 years, revenue from Spanish colonial possessions in South America had already exceeded the entire rest of all revenue to the Spanish government.
The colonization of Greenland, on the other hand, paid for nothing and withered on the vine. The colony actually died out completely. It's final inhabitants starving and freezing to death in the most wretched squalor, all but totally forgotten in Europe. It wasn't until several decades after the last Greenland colonist had parishes that it occurred to Denmark to send a ship to check just how the colonists were doing. Prior to this the last ship to visit greenland was 90 year before.