[Varyon]

Something that will depopulate Earth without intervention, and the humans need ideas from others - because their own aren't working.

There's plenty of options, here. Something that attacks our crops, like the Blight from Interstellar, is a good one - you need to recruit top-tier xenobiologists from various alien species, while preventing opportunistic factions from pouncing on Earth's weakness (and also convince others that, no, you aren't carrying a plague that will wipe out all their crops*).

A highly-communicable, rapidly-mutating virus (optionally, a bioweapon, for a "We've done this to ourselves" bit - or, as a bit of a twist, an alien power that sees Earth as a threat created and deployed it) would work as well, and honestly be rather similar in how the characters approach things as the Blight scenario, above. Particularly for something Star Trek inspired, the risk of it jumping to alien species should absolutely be present. You can take inspiration from recent events, here.

An out-of-control Von Neumann swarm, like the Faro Plague from Horizon: Zero Dawn (optionally, space-capable instead of purely terrestrial, but then it's an existential crises for everyone, not just Earth), could be interesting. Again, this is something that can potentially spread to your would-be allies, making them hesitant, but can more readily result in combat encounters if that's your thing. One thing I liked about H:ZD's implementation of the idea was that the primary threat from the swarm wasn't actually its combat capabilities (although those were formidable), but rather the fact that it was ravaging the environment with its rapid reproduction - IIRC, by the time Faro revealed he'd lost control of one of the swarms, the damage was so bad the biosphere had hit a point of no return and was doomed to collapse, even if all the machines stopped functioning immediately. Something like this could also be used - but the aliens might have a solution to stop the collapse (or at least, there's hope those xenobiologists will be able to come up with something).

In all three scenarios, you can tease hints at what's coming from news reports and the like back on Earth, before it becomes an all-out emergency.

*Note here that there may be a moratorium on people leaving Earth, for fear of the Blight spreading to the crops other colonies are dependent upon. The same would happen in the virus scenario, and maybe even the Von Neumann one. So you can't take the Interstellar approach and evacuate the planet.