Note that it doesn’t dry out; it polymerizes, and the reaction is catalyzed by water, which is why cyanoacrylate glues will stick your fingertips together instantly but will not as rapidly stick plastics or metals together.
Also, your breath might help in a pinch (it's humid).
Often if one wants to make something "larger", dropping superglue, adding bicarb with a silt, blowing away and dropping another layer works fairly well (it's a bit of a brittle but still quite hard mass that is created quickly).
Then at some point I realized that I overdid it!
Easy-peasy, a file and sandpaper to the rescue, I thought.
Aand.. I spent x3 more time shaving off the excess than building it! It's super tough.