But Paul makes it clear there is no boast of self righteousness in the 'work' of believing.
Romans 3:26-27
26He did this to demonstrate His righteousness at the present time, so as to be just and to justify the one who has faith in Jesus.
27Where, then, is boasting? It is excluded. On what principle? On that of works? No, but on that of faith. 28For we maintain that a man is justified by faith apart from works of the law.
So it's impossible to say believing is a work of the works gospel that can not save. Paul says the 'work' of believing, if you want to call it that, DOES justify. It's clear as day in scripture. Only someone who is dead set on believing that Calvinism is true will turn their eyes away from these plain words.
It is Christ's faith in v27. Man is justified by Christ's faith not their own faith. Their faith comes as God's gift from His faith
[Gal 2:16 KJV]
16 Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified.