Last night, i had an incredibly hard time sleeping. is night a adverb, noun, adjective or a verb

Night is used as a noun, it is the object of preposistion

Night is a noun night
nīt/
noun
noun: night; plural noun: nights
1.
the period of darkness in each twenty-four hours; the time from sunset to sunrise.
"a moonless night"
synonyms:nighttime; More
hours of darkness, darkness, dark;
nightfall, sunset
"they did all their dirty dealing during the night"
antonyms:day
the night as the interval between two days.
"a two-bedroom cabin costs $90 per night"
the darkness of night.
"a line of watchfires stretched away into the night"
literary
nightfall.
2.
the period of time between afternoon and bedtime; an evening.
"he was not allowed to go out on weekday nights"
an evening appointed for some activity, or spent or regarded in a certain way.
"wasn't it a great night out ?"
exclamationinformal
exclamation: night
1.
short for good night.
Origin

Old English neaht, niht, of Germanic origin; related to Dutch nacht and German Nacht, from an Indo-European root shared by Latin nox and Greek nux .

Cis definitley the answer