I see the problem, but hopefully the intended message was communicated.
I do understand what you were tying to communicate, and I hope you don't take this personally, but what you were trying to communicate is nonsense
. It CAN'T happen. "Before Time" is a contradiction, it simply makes NO SENSE. You are trapped in a line of thought, for understandable reasons, because ALL of your experiences in life are related to "time" and you are having difficulty escaping from this mode of thought. Most people do too, don't feel bad. BUT IT'S INCORRECT.
"Before Time" is an obvious contradiction, and so you MUST abandon that mode of thinking. It goes nowhere. Let me give you some examples:
a) What is North of the North Pole?
b) Can you imagine something that is both perfectly Black and perfectly White at the same time?
See? Just because you can ask the question does NOT mean the question has any significance or validity. The questions themselves DON'T MAKE SENSE.
Speaking of time though, I have wondered if in fact it began with the expansion of the singularity OR if it is more reasonable to conclude that it began prior to that at say the initial point that began the formation of the singularity.
This is an extremely deep question about the nature of reality. The answer is not fully known, but science is not
completely ignorant in this regard. We DO know some things about the answer, both from conceptual viewpoints AND from mathematical constructs.
Gravity and matter are obviously related. Gravity only works on matter, and only matter emits gravity. There is a linkage between them that CANNOT be bypassed. A symmetry exists and although we can describe
the symmetry, we cannot fully explain
it with current theories.
Gravity and time are also related. Time slows down as gravity increases. We can observationally verify this, and General relativity predicts this. Experimentally it can be verified to 14+ decimal places.
Currently, it is strongly suspected that all three quantities (matter, gravity and time) all came into existence at the Big Bang. That is to say, at T=0, at the instant Time began, matter and gravity also
began. Another way to think about it is that the decoupling
of gravity and matter caused time to come into existence. They are linked and none of them can exist without both
of the others.
At the moment we do not have a Theory of Quantum Gravity, but such a theory should describe the nature of the decoupling of those three quantities. General Relativity (which is a gravitational theory) breaks down (starts spitting out infinities) at 10-43
s after the Big Bang. At that point, quantum effect become dominate. So we simply don't know what occurred before that point. Quantum Mechanics includes everything BUT gravity, and GR simply cannot be quantized, so currently we are screwed trying to describe things before 10-43
s. (We can still mathematically ad-hoc some parts of those events however, because certain things MUST be true, but it's sloppy and unsatisfying)