I imagine the sound of the mice is quite disturbing. If this continues it might not be long before they invade your living space. I wanted to offer a few thoughts as this has been going on for over a month. You shouldn't have to live uncomfortably.

I know you mentioned you do not want management to see the mess in your apartment. Is it in a state where it is a violation, or are you just uncomfortable with it? If it is the former, take the time out to handle the mess. You don't want to lose your place. Most contracts state management can come in uninvited anyway. They may do that if someone else reports the mice. The cleanup doesn't need to be perfect. Just good enough.

If the situation is just that you are uncomfortable with it, maybe clean a bit, but throw your energy into challenging your thoughts. I worked in property management and I saw all kinds of truly messy places. The situations that were truly an issue or shocking were very few. The most important thing is living in a comfortable space free of pests, not what a stranger thinks of your cleaning skills.

I know you have a lot of boxes and you want to break them down and recycle them. That takes time, but you can knock out a huge pile in an hour. My husband does this for us all the time. You can go this route, but you could also consider this a minor emergency. Maybe this one time you just haul the boxes to the dump? Or maybe you can flatten them all out and put them in a stack in one room for now.

Cleaning can take time, but you can get a lot done quickly if you focus. I play upbeat music to help me along. I have a lot to clean in addition to shuffling other tasks every day. I never have long stretches of time to do it. I make a list and just rock out one thing at a time and then move to the next. Your apartment doesn't need to be spotless, just picked up enough for maintenance to walk through safely. Nothing should be in a hazardous state and you shouldn't have anything rotting lying around. Make your must do list and just do it. If you can do your work work while your jerk neighbor is doing his thing early in the morning and then do your cleanup while you'd typically be working.

This is all very doable in a few hours for an apartment. Stay focused and get this done. Mice means mice feces and they bring that into your home. That's unsanitary and definitely unpleasant even if it is just in your walls, the air circulates. Maybe ask your dad to pop by and help with the boxes or something, but start looking at this as easy work. You'll feel much better when this is done and you aren't losing sleep to this issue. Sleep is critical for your mental health. Fight for it.