Rn, the answer is in Romans 3 & 4.
In Romans 3:28 Paul says that we maintain that a man is justified by faith apart from the works of the Law. In verse 20 he had introduced this thought by saying by the works of the Law no flesh will be justified in His sight...
In Chapter 4 he expands this to all works in terms of Abraham. He says in verse 2 If Abraham was justified by works, he has something to boast about... But then he cites that famous passage in Gen 15:6 where it says, Abraham believed God, and it was reckoned to him as righteousness.
This is followed by an explanation in 4:4 -- ...to the one who WORKS his wage is not reckoned as a FAVOR, but as what is DUE. What is the definition of grace? Don't you say that it is "unmerited FAVOR?" We have this verse contrasting WORKS versus GRACE (Grace= Xapis). This verse uses exactly the same Greek word as we normally translate GRACE. One doesn't receive grace by WORKS. That is clear, don't you think?
Then comes the passage we are discussing: Ro 4:5 - However, to the man who does NOT WORK, but BELIEVES God who justifies the wicked, his faith is credited as righteousness.
According to this chapter, "How is one to receive the grace that justifies?"
Not by WORKS. That is clear.
But by BELIEVING. That, too, is clear.
Therefore, BELIEVING is NOT a WORK.
As 4:13 says, It was not through law that Abraham received...but through the righteousness that comes BY FAITH.
Rn, this is so clear that it is irrefutable. There is no way one can see this passage teaching that BELIEVING is a WORK. It contrasts WORKING and BELIEVING.
So, the answer to your lead in question is in verse 24 for us who believe in HIM who raised Jesus our Lord from the dead. It's not faith in faith, it's faith in Him who raised our Lord Jesus.