I agree actually with your first proposition, if faith was something that we did, an act of man; but faith is a gift from God, something God does in and for us; no one chooses faith, faith comes (as the Apostle says) "by hearing, and hearing by the word of Christ"; which is why Lutheran confess in the Large Catechism:
"For neither you nor I could ever know anything of Christ, or believe on Him, and obtain Him for our Lord, unless it were offered to us and granted to our hearts by the Holy Ghost through the preaching of the Gospel. The work is done and accomplished; for Christ has acquired and gained the treasure for us by His suffering, death, resurrection, etc. But if the work remained concealed so that no one knew of it, then it would be in vain and lost. That this treasure, therefore, might not lie buried, but be appropriated and enjoyed, God has caused the Word to go forth and be proclaimed, in which He gives the Holy Ghost to bring this treasure home and appropriate it to us. Therefore sanctifying is nothing else than bringing us to Christ to receive this good, to which we could not attain of ourselves."
It is through the Means of Word and Sacrament that the Holy Spirit operates to grant us faith, apart from ourselves, by the grace of God; Christ has instituted Means, this is why He has commissioned His Church to preach His word, to baptize, and to celebrate the consecrated Supper of His very own flesh and blood.
-CryptoLutheran