Well, the moon is a necessary part for further colonization.. Future colonists would need a mining base for metals and other minerals. I think I've read somewhere that your NASA is planning to return men to our moon, so become stepping stone for future manned attempts to mars.. And what about TERRAFORMING??
Lunar communities would be inevitably formed around these mining bases, and water would have to be imported from Earth to sustain them, at whatever economic cost..
Also, there are other ways to propel spacecraft aside from rocket fuel.. Ion drives are in experimentation nowadays i believe, nuclear propulsion, and hydrogen drives too.. if not, then tech level of the 1999ers in the Chronoverse would have possibly found a solution other than those..
Lunar outposts, not Lunar colonies, are a step (but not a necessary one) of future colonization. Indeed, the very difficulties that creating a useful human outpost on the moon is a good indication that Chrono Earth didn't colonize anywhere else. Besides the limiting expense of transporting water (and you need the resource before people could live there, so water would not have to be imported; people would have to be limited to what can be sustained), there is also the health problems associated with prolonged exposure to reduced gravity. It is fairly easy to reduce these effects over short term but over extended periods of time they are critical.
Mining the moon might happen, but this would have to largely be a mechanized operation with as limited human interaction as possible. It would be utterly impractical to fill entire caverns with an atmosphere and miners in space-suits would be limited in movement and as such in great danger. Robots would need to do the majority of mining with humans to supervise. No communities would form around these locations for the simple reason that none would be allowed. This is for the same reason that communities don't spring up around off-shore oil wells.
It is important to note that Terraforming is scientifically possible, but it is NOT alchemy. The moon will never be terraformed (though it is possible that isolated locations might have contained "terraforming," as per the noted biodome concept). Its lack of gravity, for example, makes it impossible for it to retain and earth-like atmosphere. It has no natural water resources; it is economic suicide to bring in enough water for an entire colony, but it is effectively impossible to bring in enough water to terraform it. Importing oceans is not possible. Without an atmosphere, the moon is subject to solar bursts, meteorite impacts, and "dust storms."
Other forms of space travel besides "rockets" are quite possible, but not probable for this purpose. A ship carrying the necessary materials for a nuclear powered ship can never be sent into orbit or return from orbit; the risk is rare too great. A technical error, the ship falls apart, and entire continents are subject to unacceptable levels of radiation. The materials would need to be gathered in outerspace itself (hence, why a lunar outpost would be needed). Besides, the very nature of nuclear powered vessels make it a poor choice for lifting materials off earth; propelling one's self through use of atomic explosions is all well and good in outerspace, but the numerous above-ground nuclear explosions needed to get it off of earth would likewise be unacceptable.
Ion engines are another technology that would be wonderful for outerspace but utterly useless for getting stuff off earth. Ion engines are wonderful because, like the Orion project for nuclear propulsion, Ion engines would have a very high specific impulse. But the thrust provided would not be enough to overcome gravity, as ion engines are notable for applying force over time. In a near frictionless environment, like space, a little adds up quickly (to note, however, that Ion engines can only accelerate for around 1/2 the trip, they have to slow down for the rest). But on earth, it wouldn't even get off the ground.
The most likely means of effectively lifting matter off earth (a necessary component in colonization) would be a space elevator. We do not see any such thing in CT.
Beyond that, the Lagrangian points would be a better staging point for future colonization than the moon.
It isn't that it is impossible that humans colonized the moon or other planets in the Chronoverse, however we see no indications that this happened, we see no indications that they had the capabilities, and there is a veritable 'verse full of reasons why doing so would have been difficult. With no support and near endless opposing reasons, this does not seem to be a tenable theory.
