Genesis 1:1-3 records:
In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters.
And God said, Let there be light: and there was light.
That was day one of Creation, when light (φῶς) was made.
Genesis 2:7 records:
And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
That was day six of Creation, when Adam's body was made from the fundamental elements that make up the ground. However, his life (ζωὴ) was not made, but was transferred to him, breathed into him (as we have it depicted in the text), by God.
Light had a beginning, and Adam's body had a beginning, but Adam's life simply IS, by the same reasoning that God IS. Adam's life will continue to be, until God decides it should return to Him. Where, and in what state, Adam's life might be at this very moment, is a question for another time. His body, however, has returned to the ground from whence it came.
Egeneto and gegonen are terms that relate to what has "come into being", i.e. things that have been made, so they aren't applicable to life.
The radiant light (φῶς - created) that Jesus life (ζωὴ - not created) provides, had it's beginning when God took on a body of flesh to enter our world. Prior to that, there was the glow provided by Israel's shabby, on-again-off-again implementation of God's Principles of Life (the Law), and before that, there was only the dim glow of the knowledge of the Law that might have been passed from the sons of God to the sons of men.
Addendum
How do you understand these words in context? What is it about John's words in v4 that make you think he still has creation in mind and not salvation?
Since the introduction to John's Gospel is an obvious reference to the Creation, I thought it appropriate to point out the distinction between light and life in the beginning. Light came into being on day one, but life didn't - it IS, in the same sense that God, himself, IS. Life wasn't created, it was imparted. (more about this in question 2)
It seems to me, that John was using his readers' familiarity with Creation to present a new idea, a parallel idea.
Just like on day one of the physical creation, when the light of the sun dispelled the darkness of the void, so too, on day one of a person as a new creation (spiritually awoken), the light of "the day star" (2 Peter 1:19) dispels the darkness of the spiritual void. I have no doubts John was making these connections.
What makes you think that Egeneto and gegonen aren't related, since even humanity, and by extension human life, 'came into being' at some point.
In regard to Egeneto and gegonen, I should have given you a link before. They are both related to the same Greek word, ginomai - Strong's 1096, which means "comes into being" or "is born". The words refer to created things, things that consist of atoms, and so shouldn't be used in reference to something that isn't/doesn't.
Yes, humanity was born when Adam was created, but the breath of God, the life that animated his atoms and gave them cause to want to move. That was imparted to him by God.
This idea of "the breath of God" as the animating essence of being, is the best the writer of the passage could do to show us what he was witnessing. I do hope you can see the distinction between Adam as a mass of atoms, and Adam as a "living" being.
Perhaps the vision of the prophet in Ezekiel 37, might serve to reinforce this idea, and also demonstrate how the Old Testament is the foundation for every idea that appears in the New.
Ezekiel was witness to a most amazing sight:
The hand of the LORD was upon me, and carried me out in the spirit of the LORD, and set me down in the midst of the valley which was full of bones;
...
So I prophesied as I was commanded: and as I prophesied, there was a noise, and behold a shaking, and the bones came together, bone to his bone. And when I beheld, lo, the sinews and the flesh came up upon them, and the skin covered them above: but...
... there was no breath in them.
The bodies lay motionless on the ground, and it wasn't until Ezekiel prophesied again, as he was instructed, that the breath of God entered into the bodies and:
they lived, and stood up upon their feet, an exceeding great army.
At the conclusion of the vision, God says this concerning Israel:
[I] shall put my spirit in you, and ye shall live, and I shall place you in your own land: then shall ye know that I the LORD have spoken it, and performed it, saith the LORD.
This prophecy finds its ultimate fulfilment in the "born again" experience, when a person through faith, is made alive in Jesus Christ.