“Old growth forest” is incorrect in any formulation of English grammar that I'm familiar with. It's not about fixed phrases. It's about using an adjective+noun pair (in this case, old+growth) as an adjective modifying another noun (in this case, forest). This is a general rule that applies across the board, not an isolated phrase example.

The poster was correct in asking what a “growth forest” is, because without the hyphen, the phrase parses as an adjective (old) modifying a compound noun.

And "nowadays" is an example of that process https://books.google.com/ngrams/graph?content=nowadays,%20no...

Hyphenation is useful in phrasal adjectives, like "heavy-metal shield" (to distinguish it from a shield that is of metal and is heavy, but is not or a for example Pb) or in something like "four-day trips" (the trips last four days; they are not necessarily four in number).

In English, we're making a compound adjective so it would be very-old-growth tree.

It's one step short of the German compound noun, and we make it easier to find the fragments...

This sort of thing comes up often for me. I use extended hyphenation to declare precedence: very-old--growth tree.

ancient-growth tree