Why is there a comma between 初めて and the following part it modifies?

Question

In the sentence:

大学生になって初めて、その本の本当の価値が分かるようになった

If 初めて is an adverb, it should modify the phrase behind it, which is a rule of Japanese. So here it should modify「その本の本当の価値が分かるようになった」, but why there is a comma "、" between them?
After all, I don't see elsewhere an adverb and its modifying part are seperated by a comma. So I feel the original sentence is a little strange.

I came up with an explanation: maybe here we should see て初めて as a compound particle, which means "not until". But I think it's also Ok to see 初めて as a single adverb, and the sentence should be

大学生になって、初めてその本の本当の価値が分かるようになった

just like the sentence:

親が死んで、初めてそのありがたさがわかった

in the second explanation of 初めて from デジタル大辞泉

Answer 1

You can put the comma in either of two places as below.

大学生になって、初めてその本の本当の価値が分かるようになった。

大学生になって初めて、その本の本当の価値が分かるようになった。

The two sentences give slightly different impressions. The first simply connects two statements. The speaker became a college student (first), and (then) realized the true value of the book for the first time. The second sentence places greater focus on when they made that realization as if to say it wasn’t until they became a college student that they realized the true value of the book. The whole of 大学生になって初めて could be seen as a temporal phrase.

The difference is very subtle.

Answer 2

初めて is modifying the the sentence before the comma. Think of it as two separate phrases

大学生になって初めて

Becoming a student for the first time

(A better translation of the phrase になって初めて by jisho is 'not until I became' or 'only when'.) This whole phrase modifies the expression after the comma.

その本の本当の価値が分かるようになった

I realized the true value of the book.

tl;dr: 初めて is part of the phrase before the comma