No, we are not chosen through faith.
We were chosen by grace, before the world began. We didn't physically exist then, yet God chose us. Therefore, faith has nothing to do with us being chosen.
This is just another example of you not trusting scripture.
Rom 3:21 But now the righteousness of God apart from the law is revealed, being witnessed by the Law and the Prophets,
Rom 3:22 even
the righteousness of God,
through faith in Jesus Christ, to all and on all who believe. For there is no difference;
Rom 3:29 Or
is He the God of the Jews only?
Is He not also the God of the Gentiles? Yes, of the Gentiles also,
Rom 3:30 since
there is one
God who will justify the circumcised by faith and
the uncircumcised through faith.
Gal 3:13 Christ has redeemed us from the curse of the law, having become a curse for us (for it is written, "CURSED IS EVERYONE WHO HANGS ON A TREE"),
Gal 3:14 that the blessing of Abraham might come upon the Gentiles in Christ Jesus,
that we might receive the promise of the Spirit through faith.
Gal 3:26 For
you are all sons of God through faith in Christ Jesus.
Eph 3:16 that He would grant you, according to the riches of His glory, to be strengthened with might through His Spirit in the inner man,
Eph 3:17
that Christ may dwell in your hearts through faith; that you, being rooted and grounded in love,
Col 2:11 In Him you were also circumcised with the circumcision made without hands, by putting off the body of the sins of the flesh, by the circumcision of Christ,
Col 2:12 buried with Him in baptism, in which
you also were raised with Him through faith in the working of God, who raised Him from the dead.
2Ti 3:15 and that from childhood you have known the Holy Scriptures, which are able to make you
wise for salvation through faith which is in Christ Jesus.
1Pe 1:5
who are kept by the power of God through faith for salvation ready to be revealed in the last time.