Is for the first time an adverb phrase?

"For the first time" is not an adverb phrase. It's a prepositional phrase functioning as an adverbial phrase.

Here's why:

* Prepositional Phrase: It starts with the preposition "for" and ends with the object of the preposition, "the first time".

* Adverbial Phrase: It modifies the verb of the sentence by telling us when the action happened.

Example:

* "He went to the store for the first time."

Here, "for the first time" tells us when he went to the store, acting as an adverb modifying the verb "went".