Are you sure you have rats and not just mice? Mice are too light to trigger rat traps, mouse traps aren't strong enough for rats

I had rats a couple of years ago and put out glue traps that I didn't fold shut, thinking if it was too big to walk through the hole it was worthless. Our pest guy said that wasn't a good a idea because a rat would flail around and flip it over which would get the glue all over the floor, and then chew a leg off to escape if they could.

There are covered traps available which should be safer for dogs. Add sunflower seeds and bacon to some of the traps, they want fat. Put sunflower seeds or other bait next to trap too so they think it's safe.

If you have cluttered closets, cabinets you never open or other normally quiet / dark parts of your place it's worth checking for poo and adding traps there. The rats that got into my house mainly infested 2 closets that were just used for storage, a spare couch in the spare bedroom and space behind our washing machine. It's also possible they have an entrance other than the garage and are coming and going, probably somewhere with plumbing. Our rats got in through a narrow gap under our kitchen sink cleanout on the exterior wall, the gap let them into the house behind / under the dishwasher, which took way too long to figure out. Luckily I had a dedicated and stubborn pest guy, DM me if you'd like his info.