Laying artificial grass on surface with no drainage

I tested laying out some artificial grass on the roof above my outdoor space. I really enjoyed it, but it rains all year here in NY and the roof does not have any drainage (it is essentially an ornamental fixture attached to the building by iron beams all around).

Wondering if anyone here had any ideas. See attached images of how the water pools after a very big rain storm.

My idea was to build a sandbox, but I’m thinking this may be a bit much to do myself. There is electrical outlet access from up here, so wondering if an electrical pump could be a viable option?

Added a pic of the sample cut I used to test out to get an idea of what I’m going for.