Fear of Icebergs

To win a match without building any capital ships is easiest on a small (2 player) map with easy AI. Clearly a larger fleet is needed. Once you've built up a fleet, head for the enemy homeworld, destroy the defences and shipyards.

In parallel, research and build the frigate for your faction that can bomb planets, and send it to meet your fleet at the enemy's homeworld so you can destroy their home colony - that should give you the win.

This is soft-missable, because if you build a capital ship then this can no longer be achieved in that match.

This is the opposite of Go Big or Go Home (but this one is much easier) and both cannot be unlocked in the same match.

The capital ship you get given at the start of the match for free doesn't count and can be used in the game.