As much as I hate the simulation hypothesis (it contains a lot of anti-Christian implications), I think that framework can be helpful in trying to address some of the concerns here.
Imagine that reality is a simulation. As an entity in the simulation, the only possible understanding you could have of "time" is as it exists inside the simulation.
Now imagine, also, that time in the simulation is a dimension over which the simulation acts as a solver. That is, the goal of the simulation is to determine what exists at every point of the simulation state across all dimensions, including time. Now imagine, further, that the simulation isn't stepping through time, but acts in a way that it produces a complete solution "all at once". This would mean that "time" in the simulation has absolutely no correlation to anything which the designer of the simulation might conceive as "time". The designer perceives across the entire dimension of "time" at once.
This is how Scripture speaks of God. God exists outside our concept of "time", allowing Him to perceive the entirety of past, present and future at once. It also means He can act outside of time.
The smaller issue is with time. Creation is thought to have both location and size in time. The problem is that time is part of the world, part of spacetime. So, if we focus on just the time aspect of the world, we can paraphrase that "In the beginning, God created time", which seems nonsensical.
Right. Again, consider the simulation. In the simulation, "time" is a dimension of finite extent. We perceive it as having a direction, which permits us to speak of "minimum" and "maximum" values.
What doesn't follow is that the designer's actions — that is, God's actions — correlate with that dimension. We do know that God can interact with Creation at certain points, and, because time is a dimension of Creation, those points have a dimension of time. Thus, when Scripture says God did something "in the beginning", it refers to the temporal component of where an interaction occurs within Creation.
Note that Scripture does not say "In the beginning, God created time". Certainly God Created "time", as God Created all things that are part of the universe, but trying to place the creation of a dimension within itself is an exercise in madness. A better way would be to understand that "time", to us humans, has a direction, and, more importantly, is finite. Thus, when Genesis 1 says "in the beginning", it's establishing several things. First, that God is outside of time. Second, that God Created time and (from our perspective) "set it in motion". Third, that we are about to learn about other interventions which can be placed in time, which happened at or near the lower boundary thereof.
It's also worth noting that "created" is perfect tense. Thus, it isn't wholly unreasonable to read the passage as "in the beginning, God had created...". The following verses make it clear that very little exists as of Genesis 1:1 (no stars, no land, no light), but it seems quite reasonable to read Genesis 1:1 in two parts; first, that God is the creator of time and space, and second, that the following verses describe events which happen "in the beginning" (of time).
The larger issue is with causality, which also, I should like to think, is part of the physical universe, given that it has very real physical mechanics and constraints just like everything else. However, the concept of God Creator already contains causality, it implies God is the cause of the world.
Correct, but this is actually a firm refutation of atheism. Again, God is outside of our reality. As such, He can impose His will on Creation, which includes acting as a First Cause.
Without God, no First Cause can be established, because every effect must have a cause, ad infinitum.
Actually, one part of your statement is faulty; the "very real physical mechanics and constraints" are, in a sense, illusory. Creation acts according to God's Will, and while it is normally God's Will to maintain things in an orderly manner (in the form of "physical mechanics and constraints"), as matters of that same Will, God is perfectly able to deviate from them as He pleases to do so. Causality is the Will of God. Certainly, He is able to impose that Will as he pleases, or to alter or retract it. He is certainly not bound to causality, nor is He bound to "physical mechanics and constraints". Rather, He is the source of such.
This line of reasoning, in my perception, is not a solution to the problem, just shifts it. Essentially, it's saying that not all parts of our world are accounted for by the Creation.
I think your reasoning must be flawed. The second sentence here is absolutely correct; God is outside Creation. To place God anywhere else would be to limit Him, and would leave open the question of why the universe (which could no longer be called "Creation", because, rather than Creating it, God would exist inside of it) exists in the first place. It is this reasoning that is "not a solution to the problem".
Again, consider the simulation hypothesis. Clearly, the designer of the simulation must exist totally outside of the simulation itself. If that isn't satisfactory, because it merely shifts the problem, well... too bad. It's not logically valid to discard the simulation hypothesis because it can't explain the designer, any more than it's invalid to discard Christianity because it doesn't explain the origin of God.
There is, in fact, no hypothesis which purports to explain reality to infinite regress, nor can there be, because such an explanation would necessarily be infinite. At some point, you have to take something on faith.