How do you posit the formation of the earth separately, from the rest of the universe?
It was millions of years after the Big Bang before the first stars coalesced.
If all matter was compressed, then expanded, "growing by more than a trillion trillion-fold in less than a trillionth of a trillionth of a second", why was the matter in the earth excluded from this Causation Event?
Well, you seem to misunderstand the Big Bang model.
First of all, the very early universe was very uniform in density (there were fluctuations, but we will get to those later). It was also HOT. For the first few minuites, the whole universe was hot and dense enough for nuclear fusion reactions to occur (which today require the cores of stars). It wasn't for about 300000 years that things cooled enough for the whole universe not to be incandescent. And it wasn't for millions of years for the fist stars to form.
I do not see a way to differentiate the age of the earth from the rest of the universe. It blew up, in the big bang,
Nope. The Earth formed billions of years *after* the Big Bang. Among other things, the heavier elements in the Earth (like Silicon, Aluminum, Iron, etc) were not even in existence before the first generation of stars went through a complete cycle and formed those elements in theies and following supernova.
and was suddenly, almost instantly, expanded trillions fold to fill the universe, without the need for slow gradualism. Light and other rays expanded at this same 'rate', in this cosmic creation event. We cannot assume uniformity nor gradualism under these conditions.
The inflationary epoch that you are mentioning is even b period of nuclear synthesis. All that existed at that point was a flux of quarks and electrons. It was simply too hot for even protons and neutrons to form.
The very opposite is premised, so those conditions must apply to isotopes as well. You cannot cherry pick them out of your big bang event, and apply uniform gradualism to them, only.
Well, the heavier isotopes were not even formed from the reactions in stars at that point.
Now, one of the lines of evidence for the Big Bang is the abundance of the lighter elements in the universe, which follows precisely the predictions of the hot Big Bang. Hydrogen is, by far, the most common element in the universe, followed by helium. Elements like carbon, nitrogen, oxygen (of which our bodies are made) and silicon, aluminum, iron (of which the Earth is made) did not even exist after the period of nuclear syhtnesis finished.
Another very important line of evidence for the Big Bang is those small fluctuations. As with everything in the Big Bang, they happened everywhere and eventually grew into the galaxies we see today. They also left their mark on the background radiation, so the CMBR is a very good record of the condition of the universe when it had cooled enough to be transparent to light. Because those fluctuations are the result of even earlier processes, the CMBR gives some insight into even earlier stages of the universe.
But this was *long* before even the first stars, let alone the first galaxies. The Earth formed a long, long time after that.
