Warning: Epic has clearly thought of Tilted Town as a non-build area and using one of these methods below could cost you a ban for exploit.
When a developer prohibits something, the very first reflex of the community is to find a way around the ban. So when you deprive the Fortnite community of its most emblematic mechanism, the building system, you must expect it to redouble its ingenuity to recover it.
As expected, less than 24 hours after the addition of Tilted Town to the game, at least two methods already exist to allow players to build in the area.
Interestingly enough, both consist in bringing your character into the area without walking. Apparently, the building ban have been coded to be applied only to a character crossing the boundary of the area by walking.
The first method comes from Javas:
The method consists of building a path up to the inside of the area, going into edit mode, placing yourself exactly in the middle of two squares and removing one of the two squares you are standing on.
Why does it work? Because when a square is removed from a floor, walls appear around the hole formed. If you stands between the two squares one of these walls appears under your feet and propels you to the side, thus bringing you into Tilted Town without any moving action.
The second one comes from RémyFromMars:
Stand on a board but don't drive it, just balance yourself on it. Shot on the board to push it into the area. Your character has entered the area without any moving action. You can now build in Tilted Town.
Both methods will probably be patched very quickly by Epic. In the meantime they are only exposed here to illustrate the inventiveness of the community. Do not use them, your account is at risk and... Cheating is wrong kids!