You can do a subpanel easily enough, with only one kink.
You will only be able to run 120V @ 30A. So when your feeder comes in, you will need to separate ground to the ground bar, neutral to the neutral bar, and you'll have 1 hot left. You'll have to split the hot to both "hot" lugs. At that point 240V loads won't work and you must not use multi-wire branch circuits (MWBC aka shared neutral).
Check the main panel and make sure the white wire is on the neutral bar. If it's on one side of that 30A supply breaker, move it to the neutral bar. It is OK to use only one side of the 30A 2-pole breaker.
in fact 30A 1-pole breakers aren't worth buying because they're used by almost nothing.
You can use that subpanel you have, but since this is an outbuilding, you need a "main disconnect switch". You can go get an air conditioner disconnect or a pricey 30A rated switch *if you really want to*, but the easier way is to install a "main breaker" in the panel. And the easiest way to do that on a main-lug panel is to install a 2-pole breaker in the top left, bolt it down, and backfeed it. The value of the "main breaker" does not matter since it's just a disconnect.
Like I say, you pigtail 2 wires off your hot wire, and split them to the "main breaker". If your breaker is listed to have 2 wires per lug, you can just land on one of them and have a jumper to the other one.
Then you use it just like normal.
By the way, my whole 1000sf cottage runs on 30A/120V. So it's perfectly usable.