Fundamentally what you are talking about is the ancient question: If a tree falls in the woods and nobody is around to hear it, does it make a sound?
I view reality as completely separate from the mind; that is to say, a tree can fall without being observed and still make a sound. In addition, two observers could agree that a tree fell and made a sound, *and be wrong*. In a way you could define reality as that which would occur regardless of observation or understanding. This is due to the observation that minds can be mistaken about reality, and that unexpected and unknown events can occur that later interact with those minds. I realize of course this can be explained away if we presuppose some omni-mind, but that wouldn’t be justified at this point.
You talk about necessary truths that must be true in all possible worlds at all times. I don’t agree that this is an accurate assumption for a variety of reasons. I could point out concepts like a Bose-Einstein Condensate or quantum entanglement that blur the lines between when objects are distinct or not, but that would just muddle the issue. In the end, when a philosopher says that a truth is necessary they are saying I don’t understand how it could be otherwise. It is an argument from ignorance, and is invalid.
For example, picture a reality where 1+1=3, where A = ~A; can you do it? Does it make sense? Well too bad, it is real! Perhaps if you were smarter (or less sane) you would be able to picture such a reality, but your ability to understand such a thing has no bearing on it being real.
Now about your second point; Yes, the abstract process of counting and the assignment of numbers is based on the mind. However you provide no compelling argument that such assignments are necessary for the functioning of such a reality. In fact the abstract concept you envision has no manifestation in the reality whatsoever; that cube and ball are actually made up of the field interactions of subatomic particles and on the atomic level are lumpy, jittery, hazy zones of probability that are nothing like you envisioned. To suggest your concept of a cube is at all required for those atomic structures to take a form you would identify as a cube is lunacy.
Abstract concepts don’t require physical reality to exist. But then again, they don’t really exist in the strict sense of the word. To conflate the two concepts is a gross misuse of terminology.
Now for your last point: The laws of physics are not based on mathematics. Logic and mathematics are based on observations of reality, the descriptions of which are termed the laws of physics. Before we had any understanding of logic, mathematics, or physics, the universe functioned just the same. To claim that a mind was necessary for reality to exist is begging the question.
It is also completely untrue that every atheist accepts that there should be at least a single originator or uncaused cause. I for one disagree, because while all of our evidence points toward an origin for our reality, I have no basis for concluding that the behavior we have observed of our reality must necessarily hold true for its origin. For instance time itself is theorized to have come into existence in the origin event, so there is no reason to expect that before that event has any validity whatsoever. As cause and effect also require time to be meaningful, we cannot assume such things were required.
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