Hi backup, So I'm watching the replay right now and first of all I would like to point out that opening with 2 caps isn't viable and its totally not a way to go in a situation like that.
Also took him a while to scuttle the cap fac which is something u should do instantly after ur 1st cap (or 2nd if ur gonna go with 2)
Galaxy is researching all the researchs in everytier. Something u shouldn't do either. U should focus on 1 weapontype IF u can do that.
If ur going cobalts and vettes laser is the way to go.
He researchs flak frigates even tho greg is fielding ~65 cobalts.
Anyway I would either
• Skip the ice completly and jumping my cap straight to the Moon.
• Skip the ice but clear militia first.
• Gone for civ labs and colonized it but as Greg is sova rushing and there is only 3 jumps to the ice from his Hw this would be very stupid. Civ labs as opening in general is stupid if ur not eco slot so I don't advice you to do this.
I'm in good mood today so I'm going to show you with pictures what I woulda done with the roid next to the terran.

Okey by moving it to the edge like this and not just sending it u save some hull and shieldpoints.
Why U need it to lose as little as possible is because I would send it totally alone.

Okey when it arrives in the well of the roid, it will have ~30-40 antimatter. U need to run around the well with it for a while, the best way to do this is shift commands like I show in the picture.
When It got 90 Antimatter, u colonize the planet, upgrade it's infrastructure and a defense turret close to the roid/moon facing the krosov(siege ship)
It will kill the krosov and the krosov won't have time to bomb the planet and then u can scuttle the colony frigate and the turret will finish the cobalt aswell.
Just by looking at the map we can see that it favors Greg alot. But this is almost 45minutes in and Galaxy haven't colonized that ice.
If u decide to not colonize it, which U should do atleast before 30minutes in that situation IMO. Anyway if u choose not to, he should aim for the dessert planet connected to gregs hw and set up a forward base there, Trying to force the opponent back.
However the ideal thing to do in a map situation like this is to skip imo.
He shoulda gone straight for Moon, sniping the roid next to the terran as I showed in the pictures and when he wouldn't been in a situation where he would lose roid by going civ labs, i.e. when his fleet got a nice strenght, I would have my opponent scouted and try to colonize the ice's and the volcanic.
The terran could be colonized using 6-10 scouts and a couple of vettes with a colony frigate. Killing the krosovs, colonize the planet and then use the remaining vettes+scouts to kill the lrm while setting up turrets(2-4) for the flak/Kodiaks/cobalts.
Conclusion.
•Galaxy seems quite clueless what to do here.
•He lets Greg eco. But he is neither ecoing and colonizing or going for a stronger fleet.
You should pick one, I would do the latter.
•He wastes TONS of resources on research he isn't getting any big benefits from.
•He isn't moving fleet.
•He is not scouting.
Also, ALWAYS expand towards ur opponent. The cap should go the way ur gonna fight instantly and not any other way.
Like an adjecent Terran in the other direction. That Moon is a REALLY good chokepoint as the only way the opponent woulda gotten to you would be trough a dessert and a ice. By the time that would happen U coulda taken the first ice.
So I would focus on Moon and the backroid for logistic slot.
With the amount of Cobalts greg was fielding he shoulda gotten LRM way earlier then 30minutes+ in.