Unlike in real life, in Godot children get ready before their parents. Check out the documentation here. If you print a variable on _ready it’ll always be the initial value (or null, if no initial value is defined). Setting an export variable from the parent will work, but it won’t influence printing that variable in _ready.
Thanks for the answer, I actually I figured out something else last night. The approached I took is to instantiate the HUD scene / node programatic, then I assigned a value on its script variable then I added that instance as a child of the parent scene.