The Holy Spirit does not cause faith, one must show faith to receive the Holy Spirit and be baptized in the first place. It’s all throughout acts. No I do not think we have any part in the saving, it is all God, but faith is not a work. In fact the Bible says we are saved by faith apart from works so that none may boast. Faith isn’t a work, and we are still required to express faith to be saved. You would be slandering the character of God to say that he chooses who will have faith who won’t. Hebrews says in 7:25 that he is able to save those who draw near to God through him, as in those who’ve already shown faith. Hebrews 4:16 is a call to draw near to God to receive grace, insinuating that we have a choice in doing so