Actually, the word "our" is supplied by some translators and is unnecessary as it obscured the meaning somewhat. Here is my literal translation of the first part of Heb 12:2 (eg, NASB, NIV, ERV, ISV, LSV, NAB, NHEB, WEB, YLT, etc.)
looking to Jesus, the founder and perfect of the faith ...
The phrase "the faith" is almost a technical phrase in the NT, being a short-hand for the entirety of Christian life and teaching and the faith of Jesus:
- Eph 4:13 - until we all reach unity in the faith and in the knowledge of the Son of God, as we mature to the full measure of the stature of Christ.
- Acts 3:16 - And on the faith in His name, this man whom you see and know, His name has strengthened; and the faith which is through Him has given to him this complete soundness before all of you.
- Acts 6:7 - So the word of God continued to spread. The number of disciples in Jerusalem grew rapidly, and a great number of priests became obedient to the faith.
- Acts 14:22 - strengthening the souls of the disciples and encouraging them to continue in the faith. “We must endure many hardships to enter the kingdom of God,” they said.
- Gal 3:14 - so that the blessing of Abraham might come to the Gentiles in Christ Jesus, so that through the faith we might receive the promise of the Spirit.
- Rom 4:11 - And he received the sign of circumcision, a seal of the righteousness of the faith that he had while in the uncircumcision, for him to be father of all those believing while in uncircumcision, for the righteousness to be credited also to them,
- 1 Tim 4:6 - Laying before the brothers these things, you will be a good servant of Christ Jesus, being nourished in the words of the faith, and of the good teaching that you have closely followed.
- 1 Tim 6:12 - Fight the good fight of the faith. Lay hold of the eternal life to which you were called, and also did confess the good confession before many witnesses.
Thus, of the OP's options, I would select #1 but this does not completely exclude option #2 as "the faith" is useless to all unless we make it our own.
APPENDIX - More material
The same phrase, "the faith" can also be seen as a shorthand for the phrase “the faith of Jesus” which occurs five times. Rom 3:22, 26, Gal 2:16, 3:22, Rev 14:12. In all cases the Greek “ho pistis Iesou” (note the genitive) can be translated either as:
- “Faith in Jesus” meaning the trust we have in Jesus to save us because we cannot do it ourselves. That is, we allow Him to do for us that which we cannot do for ourselves.
- “Faithfulness of Jesus” (more literally correct) meaning the trustworthiness and faithfulness of Jesus Himself that He exercised on our behalf to save us; and that we imitate in order to receive the merits and benefits of Jesus. See especially 2 Tim 2:13.
Seen another way, "the faith" can be taken as an abbreviation of "the faith of Jesus", or, "the faithfulness of Jesus" (same thing in Greek). In the New Testament the phrase “the faith/trust in Jesus” (“ho pistis en Iesous”) and in all cases the phrase is used as the basis for the Christian life and/or a cause for celebration and noted by others. Gal 3:26, Eph 1:15, Col 1:4, 1 Tim 1:14, 3:13, 2 Tim 1:13, 3:15, Heb 11:6.