I have recently been considering the significance of God calling himself (or themselves, at that point) I AM.
God also calls himself the first (and the last).
If we can derive from the above that God was the first I AM -and we know that we are also I AM's -and then consider when physical life first contemplated "I"...
we might begin to understand the nature of God.
To say I AM requires awareness that you exist in some state -and is a bit of a house of mirrors from there -and perhaps leading to there.
The human mind receives an image of its surroundings through its body -sight, touch, smell, etc -and projects itself onto its surroundings by its body.
Between receiving and projecting is processing.
"I" is a processor. "I AM" is the processor being aware of itself -sensing itself.
(We did not process our own processor -we only employ it -first without awareness -then with awareness. Then we self-program to a degree.)
If "I AM" is without beginning, then "I AM" has always been aware of "I AM" to some degree -but to what degree that is irreducible, I do not know.
The essence of "I AM" would be signal and report.
If "I AM" is a creator, then "I AM" has made more of himself of which to be aware.
Signal and report have compounded -having always been able to do so.
(In other words...
Joh 1:1 In the beginning was the Word, and the Word was with God, and the Word was God.
Joh 1:2 The same was in the beginning with God.)
We see from some forms of life that awareness is possible without self-awareness -so the question then becomes whether or not God was aware before self-awareness.
To say one is eternal -and has always been -is not necessarily the same as saying one has always known that one has always been.
Exo 3:13 And Moses said unto God, Behold, when I come unto the children of Israel, and shall say unto them, The God of your fathers hath sent me unto you; and they shall say to me, What is his name? what shall I say unto them?
Exo 3:14 And God said unto Moses, I AM THAT I AM: and he said, Thus shalt thou say unto the children of Israel, I AM hath sent me unto you.
Joh 8:58 Jesus said unto them, Verily, verily, I say unto you, Before Abraham was, I am.
So -either "I AM" was always able to declare that to himself before declaring it to others -or was always aware (signal, report, process/compound) to some degree before becoming self-aware.
I do not know the point at which "I AM" was irreducible -but it is apparent that "I AM" increases (or subdivides the infinite -or the "One").
Joh 10:30 I and my Father are one.
Joh 14:20 At that day ye shall know that I am in my Father, and ye in me, and I in you.
Isa 33:10 Now will I rise, saith the LORD; now will I be exalted; now will I lift up myself.