I have 2 options. A) Noun B) adverb then what should be the answer.
You can test each possibility by substitution with words that you are confident are nouns, adverbs and so on.
Noun: “it’s time to go * car” - this doesn’t work.
Adverb: “it’s time to go quietly” - this is grammatical, but quietly provides the manner of going while home in the original quote doesn’t.
Preposition: “it’s time to go up” - this is grammatical and carries something of the sense of the original.
So “home” acts as a preposition in your example (as noted by several commenters to your question).