You are certainly right. Faith without works is dead.
Remember the parable about the guy who got one talent and buried it? He didn’t produce anything, so his master was very angry. The guy with one talent was told he could have at least placed the money in the bank to gain interest. I take this to mean the guy could have at least supported those, the guys with five and two talents, who were putting their faith to work.
Nevertheless, faith is the critical first step.
For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast. -Ephesians 2:8,9
That’s why I believe a dying man can repent at the last instant of life and still be saved, by faith, without works.