I understand your point. I think to the thread starter, he combined both believing and doing as part of faith. That allows him to have the opinion that it has always been faith alone that saves even in the OT.
For others like yourself and me, we distinguish between them. Faith is believing God, works is what you do after you believe God.
Noah not only had to believe God that there would be a flood, he also had to build the ark after he believed God. If he believed God that there will be a flood, but choose not to build an ark, he would have perished like the rest.
No doubt the ark is suppose to represent Jesus but it does not mean Noah can say like us now, "I believe in Jesus for my salvation and cease from my works". If he adopt that view, he would still have perished like everyone else.
Likewise for all the Jews in the OT, they have to get circumcised, they have to bring the lamb every time they sinned, to get saved in the end. All these are considered works, even though we now know that the lamb represents Jesus. That still will not excuse them from those works if they want to be saved.