Here's why:
* Prepositional phrases begin with a preposition and end with a noun or pronoun (the object of the preposition). Examples include "in the box," "on the table," "with a friend."
* "For the first time" is an adverbial phrase because it acts as an adverb modifying a verb. It tells us *when* something happened.
For example:
* "She sang for the first time."
* "sang" is the verb
* "for the first time" tells us when she sang, acting like an adverb.