370,000 years after that, it cooled down enough to finally let protons bind to electrons, and the first atoms formed (99% hydrogen, 1% helium).
100M years after that, much of that hydrogen gas collapsed into stars, which underwent nuclear fusion to produce helium, carbon, nitrogen, oxygen, and other heavier elements up to iron. Some of those stars went supernova and released their enriched guts out into the universe.
After billions of years of that, we had enough heavier elements to form rocky planets, of which one is the planet we're on now.
Somehow on this wet rock, organic molecules formed and found ways to replicate themselves inside of membranes. A billion years after this wet rock came into existence, some of these replicating membranes bound to each other and started to act in harmony to ensure the continued replication of the whole group of membranes.
For another billion years, these groups of self-replicating membranes got larger and more complex. Eventually, one of them grew opposable thumbs, a large brain, and started to make tools. Those hairy apes, my ancestors, against all odds, for millions of years, fought against wolves, tigers, the elements, starvation, and each other to form an unbroken lineage that led to the existence of my parents.
36 years ago, my parents made love, and from half a billion sperm, I was the fastest. I was an accident, in both the unplanned pregnancy sense of the term and the truly cosmic nature of my improbable existence.
You want me to justify my existence? My amigo, after all that, I don't need to justify anything. I won the lottery of lotteries. My moral framework is OMG WTF I'M HERE. I'm just here to make the most of it and enjoy my 80+ (cross my fingers) trips around this boring run-of-the-mill hot pulsing orb of gas.