To all those pointing to Discover, R’ Mechanic, R’ Kellerman, and other such figures and/or organizations: These “proofs” may satisfy some, but really bright critical thinkers can easily take apart these supposed “proofs” as to God’s existence and the divinity and truth of the Torah very easily.
For such bright thinkers there usually is no proof. There is belief and a decision that a Torah observant lifestyle makes the most sense and is the most productive and fulfilling form of life. Good intellectual taamei hamitzvos sefarim may help with that. Try R. Hirsch’s Horeb. Also try some of R. Solevetchick’s works, like Halachic Man. A bright person can argue with these as well, but with bright people, the only option is to get them thinking. The choice in the end is theirs – as it should be.