This morning I was wide awake before sunrise.
Erm. Not sure ASCII art would work here, so… “I” is the subject, “was awake” - nominal verb, “wide” - adverb modifying verb (it modifies “awake” rather than “was”, but “was awake” is the verb of the sentence, even if “awake” is an adjective as a form of speech - unless you prefer to call “awake” the adjectival predicative of the subject, but come on, we’re talking about primary school…), “before sunrise” goes together and together forms an adverb of time.
This may be confusing because in English, parts of the sentence have mostly the same names as parts of speech, even if they don’t exactly (or always) correspond. For example, “awake” is not a verb as a part of speech, but “was awake” is a nominal verb. “Before sunrise” is not a single adverb as a part of speech (“before” in this case is a preposition, “sunrise” is a noun), but a single part of the sentence, known as adverb.
Additionally, the same words are not always the same parts of speech. Let’s take “before”:
“I’ve never seen you before,” - here, it’s an adverb (“when?”)
“I saw you before Christmas,” - here, it’s a preposition (“before what”) - as a part of speech, even if adverb (along with “Christmas” in “before Christmas”) as a part of the sentence
Admittedly, having learnt this on a different language first helps.
I think if you say “I” is the object, “was awake” the verb, “before sunrise” an adverb modifying the verb", “this morning” also an adverb modifying the verb, “wide” yet another adverb modifying the verb, it should be fine.