Beta (East) to play
Beta will win in four turns if Alpha plays "normally" or in five turns if Alpha stalls annoyingly.
Beta wins by catching Alpha's large ship in a catastrophe and then invading with a direct assault. Alpha can't save their g3 by trading it for red or yellow since Beta can also destroy a y3 or r3 in a catastrophe. Building y2 looks like a promising defense for Alpha at first (a move I didn't give enough attention to until Josh Kronengold brought it up). But it won't work out:
Beta will destroy Alpha's g3 on their next turn, and Beta can then invade Alpha's home with a y3. Alpha must get a large ship in their home or lose, but Alpha can only get a large ship in time by leaving it vulnerable to catastrophe:
Alpha can't do any better by capturing the invader instead:
Alternatively, Alpha can try to prepare for the direct assault one turn earlier by getting r2, but this allows Beta to build r3:
Alpha's g3 is still doomed, and Beta is now prepared to invade with a large ship. Alpha must build r3 as well.
No matter how Alpha tries to defend, Beta either wins by fleet catastrophe or direct assault. For example, if Alpha defends with r3,
Or, if Alpha tries to defend with another ship,
This position was submitted as a possible puzzle by SDG user Draw5PlayAll. The analysis is mine.