I do believe His faith saves us...from faith to faith. But the operation of His life in us requires that it is Him living in us. And that is not accomplished for us. We have to learn to walk in it. We learn to put off the old man and to put on the new man.
I believe that only through/by Him living within us, can it be brought-forth in us, and that is the only way it can happen to us. We learn, but do so only BECAUSE He has saved us and resides within us. Otherwise, we will never come to true spiritual knowledge/understanding. However, we do have to be edified/taught of Christian doctrine, through which, we increase in knowledge and believing. From that, those saved will gain a desire to conform to Christian doctrine, but they will understand that it comes from their salvation and faith and will not bring them salvation. The unsaved, on the other hand, will perceive it in the reverse - that they have to do them in order to become saved. That perception comes from being under law and not grace.
If we possessed a fully mature faith upon believing, why do we still sin? Why do we doubt? Why do we fear? Why do we resist? These things do not please God, and so cannot be of faith because without faith it is impossible to please God.
We do not possess a mature faith upon believing, we are believing BECAUSE of receiving Christ's perfect faith - His faith in us brings about our believing in Him.
To doubt, to fear, to resist, etc., are all human qualities. That we have them doesn't mean we aren't saved nor haven't been given faith as we all still "see through a glass darkly" and will continue to do so until the day of Christ.
That we have faith is God's work, not ours, and comes with being saved/born again - that also being His work.
No one can fully understand nor believe in all of the doctrines of Christianity immediately after salvation, and that is what gives rise to the concerns you mention, however, through the Holy Spirit, and by the edification of the saints by the saints, we do continue to grow over time in the knowledge of, and faith in, those doctrine.
In salvation we have faith in believing that we are under the wrath of God and that believing in Jesus is sufficient to assuage God's anger and grant us peace with Him. We don't suddenly believe all that Jesus believes. We do however have the mind of Christ which lends itself to finding out.
It was Christ offering alone that brought peace between God and man: it reconciled saved man to God and God to saved man. The believing you mention is a proof of and a demonstration of that reconciliation, but not its cause. Everything that pertains to salvation has already been achieved by Christ on our behalf, nothing by man - we are but the recipients of it through the exceedingly great mercy and grace of God given unto those who in no way deserve it - it is fully a free gift.
We do not suddenly believe all that Jesus believes, nor have we been called to do so. Jesus is God and as God knows all. In this life at least, we cannot and will not be able to do the same.
So,there is a faith given in salvation sufficient to salvation...Ephesians 2:8. There is faith that is the outcome of the Spirit working in us...Galatians 5:22-23. And there is faith given as a gift...1 Corinthians 12:9...that is given for the edification of the body. Their source is the same, but their operation and function are different.
The only faith central to salvation and under discussion is Christ's faith. Eph 2:8 and Gal 5:22 are speaking of that one single faith.
I think the result of the Spirit working within us, manifests itself in our believing. Christ's faith is imputed only once to those saved.