Grip Strength = Forearm Size?

Hi, I was wondering whether you guys believed that grip strength has a direct correlation with forearm size. My main goal is strength training, which i’ve recently adapted my workout towards. However, I have certain size goals that I want to reach within a decent time frame. I like training grip and it would be cool if that is all I should be doing to get big forearms. Right now, I have 13 inch forearms and a relatively weak grip (almost closing CoC #1). I understand that strongman have giant forearms and they don’t do any bodybuilding exercises for them, but they are also on a whole other level of physical development compared to someone like me. I also am close to the point where I don’t have to wear straps on deadlift, so i’m working on that as well.

Anyway, as a clearer way of asking this, if I get to the grip strength point where I can:
-close #3 CoC Gripper
-pinch grip 2 45s with each hand
-farmers walk for a good 30 seconds with two 225 barbells
-deadlift over-under with 550+ lb

would I have big forearms, or would they still show not that much improvement from where I am now?

thanks