Your own Faith / Believing is a work you do or perform to contribute to your salvation !
But Salvation is not of works let any man boast Eph. 2:8-9 !
The only Faith that saves is a Fruit of the Spirit given in New Birth:
Gal. 5:22 But the fruit of the Spirit is love, joy, peace, longsuffering, gentleness, goodness, faith,
Hence, no new birth, no salvation.
You made a couple of errors
The first is you do not define work as the bible does
Work in the bible refers to works of the law
Romans 4:1-16 (ESV)
1 What then shall we say was gained by Abraham, our forefather according to the flesh?
2 For if Abraham was justified by works, he has something to boast about, but not before God.
3 For what does the Scripture say? “Abraham believed God, and it was counted to him as righteousness.”
4 Now to the one who works, his wages are not counted as a gift but as his due.
5 And to the one who does not work but believes in him who justifies the ungodly, his faith is counted as righteousness,
6 just as David also speaks of the blessing of the one to whom God counts righteousness apart from works:
7 “Blessed are those whose lawless deeds are forgiven, and whose sins are covered;
8 blessed is the man against whom the Lord will not count his sin.”
9 Is this blessing then only for the circumcised, or also for the uncircumcised? For we say that faith was counted to Abraham as righteousness.
10 How then was it counted to him? Was it before or after he had been circumcised? It was not after, but before he was circumcised.
11 He received the sign of circumcision as a seal of the righteousness that he had by faith while he was still uncircumcised. The purpose was to make him the father of all who believe without being circumcised, so that righteousness would be counted to them as well,
12 and to make him the father of the circumcised who are not merely circumcised but who also walk in the footsteps of the faith that our father Abraham had before he was circumcised.
13 For the promise to Abraham and his offspring that he would be heir of the world did not come through the law but through the righteousness of faith.
14 For if it is the adherents of
the law who are to be the heirs, faith is null and the promise is void.
15 For
the law brings wrath, but where there is no law there is no transgression.
16 That is why it depends on faith, in order that the promise may rest on grace and be guaranteed to all his offspring—not only to the adherent of
the law but also to the one who shares the faith of Abraham, who is the father of us all,
Second the fruit of the spirit is a result of the Spirit abiding in a man
The Spirit does not abide in unbelievers
Jesus established the root = fruit concept
John 15:4-5 (KJV)
4 Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me.
5 I am the vine, ye
are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing.
The unbeliever is not abiding in Christ