This question, and ones like it, seem to defy satisfactory explanation for non-physicists. PEP is referred to as Pauli "repulsion", or Pauli "pressure", while it is simultaneously denied to be a force, or result in a force. Comparisons are made to ideal gases. Apologies have been offered for technical jargon being mistaken for the lay person's notion of "force". Copious math Is done to describe acceptable and forbidden behavior of particles. Yet none of the four fundamental interactions, nor indeed a fifth force, is said to be responsible for keeping electron clouds from overlapping too much (solidity of matter questions), or neutrons from collapsing further in a neutron star.
Ideal gas behavior is straightforward and intuitive enough. It's easy to see that many small fast moving particles exert an average force on their container and vice versa. But at the particle level (can we assume hydrogen gas in a balloon?), the same question arises: what force, during the impulse time of an H atom collision with the container wall, changes the particle's momentum? Again, PEP would appear to be the cause, because this is really no different than the solid object question. But, PEP is not a force, so how does a particle undergo a change in momentum without a force?