I mean, there’s plenty of evidence for the Big Bang, and if that’s the case then the most likely shape that falls out of the maths is a hypersphere, like inflating a balloon as others have said.
Which one it is depends on the density. There is a critical density at which the universe is flat, and our current best measurements basically allow for all three possibilities. It's just hard to say if something is flat or actually spherical but really, really huge.
A picture like this is in every cosmology textbook: https://upload.wikimedia.org/wikipedia/commons/9/98/End_of_u...
Which one it is depends on the density. There is a critical density at which the universe is flat, and our current best measurements basically allow for all three possibilities. It's just hard to say if something is flat or actually spherical but really, really huge.