Well ... for what it's worth, intellectual and/or philosophical pursuit of God has not proven profitable for anyone I know personally.
To be honest, even if you "prove" to yourself by logic or philosophy that God exists, that still isn't faith. Even the demons believe, and they have personal experience of God - and it does nothing to "save" them.
I think we sometimes get too caught up in intellectual belief and proofs and such because of the way the Scriptures are translated in English.
Faith in God does require belief, but every person I know that I've gotten into the heart of the process with them - has been an experiential process of coming to know God. Even if a person begins with intellectual belief, they need to progress to KNOWING God through experience.
Beginning this process usually starts with a willingness and sincerely seeking. Usually without challenging God in one's own pride. (God resists the proud, but gives grace to the humble.) I say usually because sometimes for His own reasons, God does intervene even for those with a prideful approach. But usually openness and humility is fruitful.
Sincerely wanting God and knowing we need him is the best frame for seeking. And once a person has experienced God, especially repeatedly and in different ways, it becomes impossible NOT to believe. It's like trying to believe your mother doesn't exist.
This has been my experience and what I know from others.