It is not impossible to become sinless but it is not a human attainment and it is not fully realized here.
Beware lest any man spoil you through philosophy and vain deceit, after the tradition of men, after the rudiments of the world, and not after Christ. For in him dwelleth all the fulness of the Godhead bodily. And ye are complete in him, which is the head of all principality and power: In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ: 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.
And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses; Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to his cross; And having spoiled principalities and powers, he made a shew of them openly, triumphing over them in it. - Colossians 2:8-15
What Jesus has done is to strip the law of sin and death of power over us by triumphing over them in the cross. What He has also done is to infuse within us the law of the spirit of life in Him (Romans 8:1-4). Sin and death are still in the world but our slavery to them is broken. We have been redeemed. Purchased out of the slave market of sin by the precious blood of God's only Son.
According to Paul we must choose to walk in the spirit (of life in Christ) rather than in the flesh (wherein lies sin and death) and, according to Paul, the disposition of sin in our bodies is never fully shaken off in this mortal life (Romans 7). A huge part of this Christian life is confessing when we sin and, rather than trying to evaluate whether or how close we are to arriving at sinlessness, strive to stay in step with the Spirit in faith which operates by love. God, through the Spirit, will do the rest.
A person who has received Christ has been given the power to become children of God and this power, the Holy Spirit of God himself, the law of the Spirit of life in Christ, is a deposit guaranteeing our inheritance. The good work that God has begun in that person will be brought to completion in the day of Christ. That person is predestined to be conformed to the image of His Son.
Good works that might be manifest are fruits of that Spirit, fruit that comes from the nourishment of the true vine. These are not the product of human effort and no boasting therein is appropriate. A human being on earth, a sinner saved by grace, must either confess personal sin or be thankful for the righteousness of Christ. A human being in heaven will demand nothing as wages for righteousness because it is not our own but Christ's.
The verse quoted in OP regarding the ability to do all things in Christ Jesus is, contextually, about Paul's ability to be content in every circumstance, whether to abound or suffer need. It is not appropriate to apply this to literally everything; such as claiming the ability to achieve sinlessness in this mortal life.
In Philippians 3 we can find the word 'perfect' used carrying different meanings from absolute perfection (like Jesus) to Christian maturity and this serves to resolve the various uses of 'perfect' applied to individuals throughout Scripture:
Not as though I had already attained, either were already perfect: but I follow after, if that I may apprehend that for which also I am apprehended of Christ Jesus.
Brethren, I count not myself to have apprehended: but this one thing I do, forgetting those things which are behind, and reaching forth unto those things which are before,
I press toward the mark for the prize of the high calling of God in Christ Jesus. Let us therefore, as many as be perfect, be thus minded: and if in any thing ye be otherwise minded, God shall reveal even this unto you. - Philippians 3:12-15
Until we see Him and are made like Him, we are pressing on.