On Jesus: We have 42 sources referring to Jesus within 150 years. These include Celsus, Tacitus, Josephus, Lucian, Mara Bar Serapion, Suetonius, Thallus, Pliny the Younger, Phlegon. Which is what you refer to. We can however also go one step further by applying the historic criteria above. The suffering of early Christians is attested by Shepherd of Hermas, Melito of Sardis, Tacitus, Dionysius of Corinth, Hegesippus, Eusebius, Polycrates, Bishop of Ephesus, Pliny, Josephus etc.

Existence of God: moral argument, transcendental argument, Kalam cosmological argument, Leibniz argument from contingency, teleological argument, argument from consciousness, argument from cosmic consciousness

Your son might be interested in reading this:

https://streettheologian.com/index.php/2022/03/22/response-to-edward-johns-someone-wrote-an-8-minute-response-to-3-reasons-god-cannot-possibly-exist-part-2/

I was an atheist as a teenager in a Christian home so I can very much relate to your son's experience.