There should be a button to begin spawning a wave of enemies. After each Tower Defense round you get a morality check where a dubious advisor comments on your conundrum (which is the - rather flawed- relation with the theme).
Are you on Mac by chance? Only the windows build has been properly tested. The UI might also have scaled weirdly if you're on very high or very low resolution, or perhaps an unusual aspect ratio - causing the button to go off screen.
Viewing post in The King's Advisor jam comments
Wait you *do* see the button? Then what happens when you press it?
As I said, the UI should be scaling fine, but it hasn't been tested above 2k or outside 16:9 so I theorized the button might have gone off screen. (Obviously its scaling with screen size, but the anchor might have been wrong). But if you both can place towers, and spawn the wave of enemies, then I don't quite get what you mean by "but nothing"...