Researchers doing simulations of balloons start with geometry in the shape of a circular balloon at the size it was manufactured, then use moving rigid surfaces to fold the balloon using frictional contact to simulate the folding that an actual machine with moving blades would use to fold the balloon. Then they simulate the inflation of the folded balloon.
These models tend to run in Explicit Dynamics because of the complex contact modeling required. You can't use the Mooney-Rivlin material model in Explicit Dynamics, so you will have to replace that will a material model that is supported in Explicit Dynamics.