Nope. The version you used (probably the NIV) added the word "your" to the verse. It is not in the actual text. The faith of that verse is NOT the faith of those whom Paul was addressing; it is the faith that exists within the working of God, which faith, is the faith of Christ - His faith brought salvation. We cannot be saved by anything we may do, including by our faith. Christ is the Savior, man is not.
It this case, I believe the KJV states it more correctly. Notice there is no "your" in the verse; notice also that faith is singular : "the faith", not plural, meaning there is only one faith pertaining to the operation of God (or "working of God" per the NIV) and salvation. Given that there is only one, it therefore cannot be referring to the faith of those being addressed, which would then have to be plural.
[Col 2:12 KJV] 12 Buried with him in baptism, wherein also ye are risen with [him] through the faith of the operation of God, who hath raised him from the dead.