Echoing other on hardware cloth.
I had a residential pest control person tell me once that mice can fit though a hole the size of a dime, and rats through a hole the size of a quarter. Mice can jump vertically about 13”, and both are very proficient climbers. Rats also tunnel(but since your floors are concrete that shouldn’t matter).
Basically, unless every exterior border or opening should be sealed off or covered with 1/4-1/2” hardware cloth or a mesh of some kind.
Rodent infestations are tough to get on top of. Cats help… but rodents are like predators. Once they discover a food source, they’ll set up camp and breed+probe for weakness.
My chickens coop to run access door is about 20” off the ground, and I removed their ladder. They can all jump up just fine without it, and since the ladder/ramp removal, we’ve had zero mouse activity in our coop. They still come into the run from time to time at night I think, but its drastically reduced. Maybe one set of mouse tracks in the snow leading to the run every few days?
Sorry you have to struggle with this!!!