Learn Russian: Ураган начался гораздо раньше.

Because the hurricane isn't starting something else, it is just happening. In English, "to begin" can take a direct object ("He began the meeting") or act independently ("The meeting began"). Russian requires two different verbs for this: the standard verb начать for when an active subject starts something, and the reflexive начаться (past tense начался) when an event simply begins on its own. The event (ураган) acts as the subject and takes the Nominative case.

Why does the verb end in -ся here, when reflexive verbs sometimes end in -сь in the past tense?

The choice between -ся and -сь depends on the letter right before it. If the base verb form ends in a consonant (like the masculine past tense начал), you add -ся, making начался. If it ends in a vowel (like the feminine past tense начала), you add -сь, making началась. Since ураган is a masculine noun, we must use the consonant form.

Could I use очень instead of гораздо to say the hurricane started "very" much earlier?

No, очень (very) can only be used with base adjectives and adverbs, like очень рано (very early). Because раньше is a comparative form meaning "earlier", you must use гораздо or намного to intensify it. This is exactly like how in English we say "much earlier" instead of "very earlier".