[Alastor Mobius Toth]

Not a problem. Always happy to get another Mabu-Ravu started.

Extra universe is pretty similar to ours circa 2001, although I suppose there's the existence of ridiculously powerful groups like Mitsurugi Group.

>Outer Space Treaty

There can be several approaches to it, I think.

The first is assuming that Nuclear-able powers actually will decide to abide by it (since UN can't really enforce it's laws, and both America and Russia are Security Council members), they can argue that the Treaty applies to terrestrial states, not an entity such as alien race, and that this is a "special" situation. To be fair, the language of the OST is somewhat outdated, reflecting the tensions of Cold War that would be end by this point.

As for countries behavior, that depends on the writers evaluation. Personally, I think that countries like Russia and China are interested in self-preservation first. In Muv-Luv, cooperating with Americans wasn't so apparent in face of their ideology-colored world view. Americans and West were still as much an enemy as Aliens. But a Russia circa 2001 might consider aliens to be a sufficient threat to ignore traditional enmities. Especially since Putin wasn't in power yet, so the Russia wasn't entirely in the "Cold War revival" mode it is now. In fact, you could argue that Russia might hop on board with American nuclear attack, because saving mankind from aliens is a pretty big cred boost.

Alternatively, legal trolling. International law is generally full of loopholes, and is open to a very broad interpretation. You can always argue that ICBMs are "ground-to-ground" weapon, and you aren't really breaking the OTS, since they're based off Earth, fire on Earth, and explode before impact, so they aren't, technically, detonating on the Moon. Does it sound silly? Yes, but this would be hardly the first silly thing done in international law.

The best way would be probably to skip Moon phase altogether. Extraverse humanity has same level of space industry, and we technically don't have the capacity to land the Moon (all this technology was lost since 1969, since nobody bothers with the Moon anymore. All this tech would have to be re-developed to modern standards). Instead, BETA land directly on Earth, and the ride starts. This way, we can also explain why nations of Earth didn't shoot the Hives down - they might have not realized that Aliens were hostile, since there was no Lunar contact.