Teamsite without subsites

Even without your IT department's mandate not to use subsites, you still have some options that could work out better than site collections would have anyway.

I would propose you use a modern Team site and create as many document libraries as you have departments, with all departments having access rights to the Site but different rights per library as desired by your user group. If your location is fairly open with its documents, you could conceivably have a situation where all departments have Read to all libraries and only Contribute to their own department's library. If some or all of your location's departments want to stay private, the unique permissions on each document library will protect those privacy requirements as long as your permission structure is set up correctly.

*EDIT* Alternatively, you could give each department its own Modern Team site and wait for Hub Sites to roll out. If Hub Sites aren't on the immediate horizon for rollout, or if they don't accomplish the everything Microsoft promises they will right away, you would need to have some fairly redundant permissions structures across each of these Team site/collections to grant whatever permissions are required department-to-department.

Hope that helps!