You don’t need to be that creative to think of ways to do this without getting into “owed sex” trap.

First thing I could think of in sixty seconds: State money can sponsor singles nights with a few free drinks for every person attending courtesy of the government. Pays for responsible security and all the appropriate safety and security.

That’s just a minute thinking, I’m sure a few hours or days work could do much better. And it’s infinitely better than just giving them money directly which will likely not drive the sort of interpersonal behaviour changes they hope to sponsor since money can go directly into the things these people are already doing with their time.