Before I even start in on this, let me ask, how did faith in Christ come to you? This is an honest question. If I sat down and heard your testimony, what events led up to you receiving Christ?
Ok now let's dive. As I mentioned above, faith ultimately is a system that God has gifted to mankind, to all of us. While I'll argue below that our willingness is crucial, right now let's break down what scripture says in regards to the origin of saving faith.
17 So faith comes from hearing, and hearing by the word of Christ. - Romans 10:17 (emphasis mine)
31 but these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name. - John 20:31 (emphasis mine)
These are pretty straight forward. Christ often said "He who has ears, let him hear" (Matt. 11:15, 13:9, Rev. 2:29, 3:13) and on the contrary spoke of not getting through to those who have become dull of hearing (Heb. 5:11, Matt. 13:15). It is with this understanding of faith coming by hearing the word of Christ that Paul writes in Romans 10:14 the following (though I'm adding the verses before which lay a proper foundation to the question and what we've been speaking of here.)
11 For the Scripture says, “Whoever believes in Him will not be disappointed.” 12 For there is no distinction between Jew and Greek; for the same Lord is Lord of all, abounding in riches for all who call on Him; 13 for “Whoever will call on the name of the Lord will be saved.”
14 How then will they call on Him in whom they have not believed? How will they believe in Him whom they have not heard? And how will they hear without a preacher? - Romans 10:11-14
Faith is a gift of God, likewise is the ability to choose (1 Cor. 4:7, John 7:17, 1 Cor. 7:37, 39, Philemon 14). God gifts us with His word, and using our will that God has gifted to us we respond to it (2 Cor. 5:11, Rom. 2:4, Rev. 3:20)...or not (John 1:12, 5:39-40, Luke 13:34, Rom. 10:12-13, 2 Pet. 3:3-5, Rom 1:18-20, Rom. 10:21, Acts 7:51, Rom. 11:15).