I'd argue that in the long run, thinking of branches as the entirety of the history before a commit causes more confusion. I'd propose that the most useful way to convey the idea of branches to new git users is to start with the concept that every commit after the initial one has one predecessor, which means that you can always trace back the history of a commit by following the predecessors back to the initial commit, and then introduce the idea of a branch as a name that refers to a given commit. Combining these two ideas means that for any commit, you can definitively state whether or not it exists in the history of the commit that the name points to, and that commits that are part of that history are conceptually considered to be "in" the branch. Then you can introduce the idea that you can "update" the commit that a branch points to, and that the only way to add a new commit is to "increment" a branch to point to a new commit after the current one it points to.
This establishes enough information for you to show how using a git repo actually works; at any given time, you're looking at one specific commit, either directly or via a branch's name. If you're using a branch, then committing will perform the "increment" discussed earlier, with the branch now pointing to that new commit. Showing how to create a new branch will naturally lead to the discussion about how you can have two branches pointing to the same commit; this lets you explain that adding a new commit without specifying a branch name can be ambiguous, which you can demonstrate by checking out the current commit directly rather than by a branch name. Once you've shown that adding a commit requires either checking out one of the branches you have that point to that commit or creating a new one, you can show that the same principle holds for any other commit in the repo as well, even ones further back in the history with no branch currently pointing to them. You can use this opportunity to introduce the concept of `HEAD` as the unique name for whichever commit you're currently looking at, and that looking at a commit directly rather than via a branch is called having a "detached `HEAD`", which means that you won't be able to make any changes without creating a branch at that point first and "reattaching `HEAD`" to that new branch.
If you're trying to teach git to someone who hasn't yet learned the equivalent of an intro to data structures class in computer science, it might be worth simplifying the concept of branches in the way you describe. If you're teaching someone who already understands what a tree is, you're doing them a disservice by trying to hide the model from them because they have more than enough to understand what a branch actually is.
This establishes enough information for you to show how using a git repo actually works; at any given time, you're looking at one specific commit, either directly or via a branch's name. If you're using a branch, then committing will perform the "increment" discussed earlier, with the branch now pointing to that new commit. Showing how to create a new branch will naturally lead to the discussion about how you can have two branches pointing to the same commit; this lets you explain that adding a new commit without specifying a branch name can be ambiguous, which you can demonstrate by checking out the current commit directly rather than by a branch name. Once you've shown that adding a commit requires either checking out one of the branches you have that point to that commit or creating a new one, you can show that the same principle holds for any other commit in the repo as well, even ones further back in the history with no branch currently pointing to them. You can use this opportunity to introduce the concept of `HEAD` as the unique name for whichever commit you're currently looking at, and that looking at a commit directly rather than via a branch is called having a "detached `HEAD`", which means that you won't be able to make any changes without creating a branch at that point first and "reattaching `HEAD`" to that new branch.
If you're trying to teach git to someone who hasn't yet learned the equivalent of an intro to data structures class in computer science, it might be worth simplifying the concept of branches in the way you describe. If you're teaching someone who already understands what a tree is, you're doing them a disservice by trying to hide the model from them because they have more than enough to understand what a branch actually is.