if you're trying to use logic, and reason, then you already (by faith) are believing that there is purpose, cause and effect, and order in the universe, so to go on from that and take the stand that all things are chance, random & chaos is "illogical" in the sense that it's at conflict with the very idea that you can think or hold a "belief" at all.
if you accept that having "ideas" and "concepts" beyond fire hot and food good signify some sort of intellectual capacity that's more than what is necessary for crude survival, that man is more in any sense than a beast, then what's left is to trade arrogance due to this assumption for humility, and ask finally "why" - because there is no evolutionary advantage to burning all this energy up, exercising one's brain with such thoughts and questions - you admit there is, then, something "more"
if the arrogance can be set aside, there is God, and there is man. the preponderance of evidence of religion all over the world in every culture and every people ought to be enough - else men reject it, holding on again to arrogance in themselves, thinking the whole of humanity is stupid and deceived. again, one needs humility.
once you accept that there is God, and there is man -- then there is only one understanding of this with a living God, actively reaching out towards man. Jesus Christ. in every other religion and belief, it's incumbent on mankind to reach up towards God, to make himself worthy to be noticed by the divine. only in Jesus Christ is revealed the love and grace of God, setting aside His glory & stooping down to be born in stupid, ignoble flesh, in order to reconcile us to God and make Himself known to us.
this takes humility too. you cannot come to God with pride, intellectual or otherwise.
this also transcends and turns logic and reason upside-down -- and i don't believe you can see it without being called by God, and having the Spirit of God Himself putting faith in you, to answer. is that a death-stroke to freewill? a whole other discussion. but tangentially, i do not see free-will as humility, and i still maintain that pride will block anyone's line-of-sight to God, until it is shattered and humbled.
i wouldn't expect to convince anyone of Christ "by reason" alone. we answer, because He first calls.