Critters can squeeze their bodies into any space their head will fit into.
Humans, not so much.
There are ways to fix and exit using flexible mesh that allows them to leave, but not return.
I watched one of those exterminator tv shows years ago and saw their setup. It was ingenious. You may find an episode or explanation on YouTube.
We had a turd of a neighbor kid who got mad at us and dumped her pet rats over our fence. The havoc they caused was a six-month battle of wills but I prevailed and they never got inside the house.
Glue traps are great if your a cold hearted so and so like me who doesn't lose sleep when they start screaming after they get stuck and before their nose does, suffocating the buggers. My husband couldn't handle it. So I had to go with snap traps.
Broke both thumbs and two fingers, but I got them put out. And replaced daily as the body count rose.
I suggest peanut butter. Just enough to coat the trigger mechanism, though. They are not stupid creatures and will steal your bait every chance they get.
For the bigger Norwalk rats, I used live traps and had a slick-sided barrel with enough water to make them have to swim...until they couldn't.
Check with your local animal shelter. They often have these things that you can borrow after leaving a refundable deposit to cover the trap should you not return it.
Again, unless you are willing to kill these things, you will never win the battle.
In the meantime, start putting steel wool in any opening you find and firmly attach metal mesh or sheet metal on both sides of the opening. Yes any left inside the barrier will die. And smell to high heaven. But you have to stop the flood in before you have a chance of beating the stragglers down.
Also, clean up anything that could be food. Secure wiring and check the insulation on any exterior wiring. They love that stuff.
If you have a zoo close by, see if they will let you buy lion or tiger poop. It will stop just about anything from coming around. And it stinks... it is poop... but you have to use everything available to win this war.
As an aside, steel wool in your weep holes, should you have any, will also help stop hornets and wasps (or bees) from entering there and nesting in your walls. Just replace it regularly as it does degrade.
Good luck. Put your game face on. This one is not for the weak willed.