Hi,
Is it possible to get a mesh to reveal itself, either on entering a zone or with a button press?
I have some meshes that I would like to grow out of the floor to build themselves, so I could either animate them under the floor and moving up into position, or have them fade on properly.
Or is it possible to animate an invisible box that occludes the mesh in some way until it is revealed?
Any ideas appreciated 
you can animate objects or you can expose single parameter from your material and then animate value to make object appear or materialize in front of player. for example set material to masked get random grayscale alpha and multiply it to constant converted to a parameter. when increasing value object will start to appear when decreasing to 0 it will disappear. Obviously that’s just example to get cool effect you need to play with material editor a little bit more
There is the basic stuff you can do just to make it visible (but this is not really advanced)
there you could add delays untill every pieces are visible
Or you could make a trigger box that start a matinee that put every block in position too. If you want to use a button in the trigger box zone, just use a Gate after the trigger box OnActorBeginOverlap or something like that.