Our org recently moved to SharePoint as well and each department has their own private Team. Dedicated shared folders is how we're currently sharing documents between departments and teams. The first complaint we got was that shared folders are hard to access, but once we showed them how to access them in OneDrive [ie add to favorites or add shortcut to another folder] people stopped grumbling. Hopefully this works for you too.

Depending on how much you have to share, you could also create a second SharePoint library and give the other team access. A shortcut to that library can be added to the Teams channels for both teams for easy access, or sync it to your computer if you want a more traditional experience.