I have a team of 10-12 users that are all using Trello. Every time I create a new board I have to manually invite all of them to participate on the new board. Is there a way to default all users in my organization to be assigned to the board when it is created?
Sounds like you want to create what Trello calls an "organization".
You can get to it by clicking on your picture in the top right and selecting Boards, then at the bottom Create an Organization.
Then when you create a new board, you can set the permissions so your entire organization can see it.