Now that the game has become more stable, Steam Workshop integration will be available soon. In fact, the Workshop page is already up: https://steamcommunity.com/app/3105680/workshop/ — but it’ll take a while to get everything running, so expect a few updates.
Current Proposal:
You will be able to upload teams, players, competitions, and many other types of content.
When uploading teams, you can choose whether to include their venues, jerseys, flags, name pools, confederations, tags, etc.
You won’t need to upload teams one by one. Team filters—similar to those in the competition editor—will let you select teams by criteria.
Note: the main site is no longer compatible with the Steam version, but you can still create and share teams for fun. https://v1.simcups.com is the exclusive site for Steam users.