New Shot of Tempest (as in, not a trailer screenshot or whatever) on PS4 Pro Website

True but, aside from the N7 (who we're not even sure is part of the crew at all), we've not seen them wearing any recognisable military uniforms or insignia either on their person, on any of the ships or shuttles we've seen or on the Mako. We've seen an Andromeda insignia but nothing which indicates that any of them are acting in an official capacity as a member of any of the militaries we know from the trilogy.

Some of them may be ex-Military but I can't see the expedition being resourced or run by the military.  I just don't see what possible reason the military would have for taking a bunch of resources and equipment and sending them off to another Galaxy never to be seen again. Particularly, when those in the know are well aware of the threat of the Reapers who threaten their entire civilization at home.

It makes sense for some concerned private citizens to have heard Shepard's claims of the Reaper Invasion, seen Sovereign's attack on the Citadel and be feeling that the world is doomed and that the best way to survive the Reaper threat is to try to colonize another Galaxy. It also makes sense, if they can, to get combat-trained soldiers to come with to defend them but it doesn't make sense, IMO, for the military to be behind the initiative in any meaningful way.