My experience is that a full trusting in the efficacy of Jesus' death to have worked my own death absolves me of anything that would hinder my faith in Him, so that I can walk in His Spirit, bearing the fruit of His Spirit in me, walking in the pre-ordained works, not conscious of sins.
I don't expect that I would ever claim to be sinless, that strikes me as foolishness and hubris, only Jesus is the proper and fit judge.
My experience has been that for a time I think that God gifted me with the faith to so live for a season, then after that season began my training to apprehend that same walk and mind through trusting in Chris on a more conscious level.
Isaiah, Jeremiah, both used words like, our transgressions testify against us, the Godly answer is, the just shall live by faith, and, we walk by faith and not by sight.
Seeing the sins of your flesh doesn't mean your new creation is tainted by sin. Standing in that faith, you will see the sins of the flesh cease. Maybe quickly, maybe through a process of time - of training - of renewing the mind.
And I'm not just talking about "not sinning", that is, abstaining from those things you hold to be wrong, but truly not sinning, meaning, a failure to be joyful, a failure to be loving, a failure to be faithful and trusting, like that.
Simply stated, He showed me through experience what walking in faith looks like, and now He shows me how to hold to that faith more and more consistently, so as to stand in His grace.
Much love!