Here is my 2 cents:

They have a process, it is slow but it does the job. So start by saving them several hours and help automate their current process. This is valuable (saving manual labor) and will already be challenging: you will have to sit with them and understand how they do it. If it takes several hours, it is unlikely that they have a deterministic algorithm for it. To create one, you will likely have to have them make a number of decisions. You can probably help them make them. The outcome should be an algorithm, as simple as possible, that can perform the assignment of associates to teams.

Once you have solved this problem for them, you can think about ways to improve the assignment. But this open a very different can of worms. What does better mean? How do I measure that it is better? You will have to define some meaningful metrics (make sure they define them or that they definitely sign off on them) to be able to compare different assignment algorithms. Because you have so few teams, it will be pretty difficult to design a rigorous experiment that helps you determine if your new assignment algorithm beats the baseline. You can always come up with some fancy algorithm but how do you prove it works better? Some associates will say they don't like the new system some will like it. Who should we believe?Not to mention that you'll want to be able to track teams easily to be able to run some analytics. Chances are you'll have to build tracking for the teams. It might not be worth your time.

I've spent months trying to do things like this. The main challenge is that the Ops team wanted something better but never wanted to invest into defining or measuring what better was.

Alternatively you can keep adding simple constraints to your model that satisfies their intuition but that's not exactly Machine Learning so I would try to not get stuck in that position.

Good luck!