I think you may have partitioned the causeless causes, which is why you find so few.
The first causeless cause is, naturally, the first cause. In science, this is "the big bang," though there is plenty of philosophy on other first causes. So far it seems unpopular to consider concepts of time which don't have a cause. You might be able to find some interesting causes there, but if we stick with what is "popular," the big bang would be it.
Once one is past the first cause, as in the cause whose time precedes all other causes, we can explore causeless causes which occur after this first cause.
I would argue an easy way to approach these is through complexity. To quote wikipedia:
Complexity characterises the behaviour of a system or model whose components interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions.
Systems for which there are reasonable higher order instructions to define the interactions tend to be called deterministic, and there's always a cause for everything in such corners. Thus, what is left as "complexity" is where all other causeless causes could be found.
Dr. Warren Weaver divided complexity into two categories: disorganized complexity and organized complexity. This was a partition. Disorganized complexity considers that which can be understood by probability and statistics. Quantum Mechanics is a clear example of this. Organized complexity is everything that wasn't disorganized.
I draw these divisions because they partition the possible places for a causeless cause in a way that is similar enough to the choices of your words to possibly offer food for thought.
- First Cause: Big bang
- Disorganized Complexity: Quantum Mechanics
- Organized Complexity: Freewill
This association, of course, is one that you may take or discard at your preference. Disorganized complexity is dominated by QM because we have beaten down all other sources of disorganized complexity through the scientific method, leaving us at a collection of deterministic systems with disorganized complexity at its core.
My claim that organized complexity is associated with freewill is one that may be heavily debated. Not everyone's definition of freewill fits here. However, I do believe they are close enough to be worth mulling over here. Perhaps the thing you are referring to as freewill here is causeless causes that stem from organized complexity, which would defend my claim that there's a partitioning going on. I do note that many systems which exhibit organized complexity, such as the weather or the oceans, are heavily personified and assigned freewill by many individuals who work with them.
So it may be that the reason we see so few causeless causes is that what we are really seeing is a partition of causeless causes, and we only partition it as much as we find convenient.
As such, I would add one more to the list. All of the complexity examples focus on systems which follow local rules. Complexity does not capture something operating on a global scale. As such, I would list "God" as a causeless cause, using a word which is very popular and heavily overloaded.
Regardless of whether one uses the terms "freewill" and "God" to describe these things, I believe this example does partition the causeless causes, and does so in a direction that may be applicable to your question.
