You can start right where he is.
The Big Bang arose at a time when the expansion of the universe was thought to be constant and limited. So, it was easy to think that eventually, gravity slowed and stopped the expansion, so everything could fall back together and explode again, over and over. See the work of Fred Hoyle.
Within the last few years, scientists have learned the the expansion is accelerating, everything is moving apart faster and faster. So there’s only ONE Big Bang.
Where did the matter and energy of the Big Bang come from?
Where did the laws of physics come from; why should there be laws of nature at all?
Mass (or energy) and momentum (motion, mass times velocity) are conserved (invariant) in all known science experiments. There is a lot of matter around, and it’s moving. How did that start?
The Big Bang begs the question: where did the original matter and laws of physics come from?
The measured physical constants are finely tuned; if there’s any change, then the conditions for human life are not met.
You will find many books and web sites where serious scientific work is documented, and where the wonderful areement between faith and reason is clearly demonstrated, like
Discovery Institute .
There is also the possibility of some harm to a person that leads them to hate the very idea of God. Theeir pain or sin can make them resist the obvious proofs of God that are everywhere from the stars in the clear night sky to the human eye.
Most of all you have to pray and fast for people. Your example of joy and peace, alongs with your reasons for confidence in God are very important, too. God does the work in His time and way; yours may only be a step along someones way, so don’t be discouraged if you don’t see immediate results.
There are literally mountains of information, but the challenge is to find intellectually honest, rational thinkers. I would start with the
Pontifical Academy of Sciences (400th Anniversary) and found interesting, thorough discussions from various sciences. See if you can find the paper: “A Millenium View of the Universe” by V. C. Rubin in the Proceedings of the Jubilee Session
God is everywhere, for those with eyes to see:
Astronomy Picture of the Day from Hubble Telescope