We cannot reason our way to God. The God of the Bible is the God of reason, truth, and history. But none of these things connect us to Him redemptively; faith does. However, sound reason is not incompatible with faith, but actually works with it to lead us to truth. Faith in God, as it turns out, is the most reasonable thing to have. All truth originates with God and therefore points us to Him (Ro 11:36). Winfried Corduan is right to write, "We do not need to be gingerly in our investigations of truth. If a belief cannot withstand hard questioning, it may not be worth holding. If Christianity is true, it should be able to withstand the hardest questions we bring to it. If Christianity is not true, we should reject it."
He goes on to say, "It must be kept in mind that it is not as easy to show Christianity to be false, even hypothetically, as some people think."
The "fool" who says there is no God (Ps 14) is a fool because he acts against sound reason, not faith. He acts against the world of evidence that communicates to all of his senses and mind that there is indeed a creator with distinct divine attributes. The testimony of history also testifies to God's existence and work. A key reason the Bible generally and the New Testament particularly are so credible is because of the massive eyewitness testimony on which they are based. Christianity happens in real time and real space. It is rooted in corroborated historical events, unlike any other belief system. It's key events and characters have been seen and heard and documented. The Bible as a historical document cannot be successfully shown to be untrue. It stands the tests of historical authenticity. Now, that being said, receiving this historical document as the Word of God requires some faith, which is the gift of God (Ep 2:8), comes by hearing His Word (Ro 10:17), and so does not come by our senses.
The testimony of conscience is also a powerful witness to God's presence in the world (Ro 2). So are our otherwise unexplainable longings for love, justice, beauty, and so forth. These come from being made in God's image and likeness (Ge 1), and they clearly distinguish us from His other creatures.