Is the act of Faith a Work ? Yes it is, and here's some reasons why
1. Because we are commanded to believe (as we are) to love one another, as he gave us commandment, 1 John 3:23.
2. To obey a command, is a work; but to believe, is to obey a command, 1 John 3:23, 24. Faith is an obeying of the will of God; therefore it's a work, and a good work.
3. It's a work, because we are reproved for the smallness of our faith: Christ said, "O ye of little faith," Matt. 6:30, "why are ye fearful? wherefore do ye doubt, O ye of little faith," Matt. 8:26. If faith were not acted by us (although the power is of God) why are we reproved for not believing?
4. It's a work, because the Saints are exhorted to exercise faith: "Let us draw near with full assurance of faith," Heb. 10:22. We are not exhorted to nothing but to that which is our duty, as it is to do a good work, as believing is.
5. It's a work, because to believe is a work of all the faculties of the soul, viz.: memory, conscience, affections, principally the understanding and will, Rom. 10:9,10.
6. To receive a thing is an act of the whole man; but to believe in Christ is to receive Him: 1 John 1:12. Therefore, to believe in Christ is a work.
7. Because unbelief is a work of darkness; therefore to believe is a work of righteousness, Tit. 3:5.
8. Because, to a good work faith is required, therefore, it partakes of the nature of a good work, and so is a part of every good work. (Heb. 11:4)
9. It's a work, because we are said to do it: If thou believest, I do believe, Acts 8:37. To believe is the action of the heart, viz.: will: With the heart man believeth. He does it as truly as he confesseth with his mouth, Rom. 10:9, 10.
10. If to confess Christ be a duty and a work (though by grace we do both), then is the act of believing a work also, and a work that we do, and is one of those works of righteousness that we have done, Tit. 3:5 with Isa. 64:6.
https://www.pristinegrace.org/media.php?id=798
See believing on Christ is a command, something which is done in obedience. Paul answered the Phillipian Jailor when he asked what shall he DO to be saved, and Paul answered Believe on the Lord Jesus Christ Acts 16:30-31
30 And brought them out, and said, Sirs, what must I do to be saved?
31 And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house.
Now interestingly enough the word believe here the verb pisteuō and its in the imperative mood which means:
Corresponds to the English imperative, and expresses a command to the hearer to perform a certain action by the order and authority of the one commanding. Thus, Jesus' phrase, "Repent ye, and believe the gospel" (Mk.1:15) is not at all an "invitation," but an absolute command requiring full obedience on the part of all hearers.https://www.blueletterbible.org/kjv/act/16/31/t_conc_1034031
Yes believing in Jesus Christ is a work done by the one obeying the imperative to believe on Him. So if we say that God saved or Christ saved us from the penalty of our sins because we believed on Christ, and God responded to our obedience and saved us from our sins, then we are in essence saying we are saved by our work of believing. Reference is made to samuel richardson, his work " Justification by Christ alone" for many of these points. 20