Learn Dutch: Ook al rommelt de vulkaan, het belooft veilig te blijven. - Even though the volcano rumbles, it is likely to remain safe.

In this structure, beloven te followed by an infinitive (te blijven) acts as an indicator of trajectory or likelihood. It means that based on current signs, something is highly likely to happen, similar to "promises to be" or "looks like it will" in English. It does not require a conscious subject making a vow.

Shouldn't the main clause have inversion after the comma? Why is it het belooft instead of belooft het?

You spotted a classic exception in Dutch word order! Normally, when a sentence starts with a dependent clause, the following main clause must invert (verb-subject). However, clauses starting with ook al (even though) are the major exception: the main clause that follows keeps the normal subject-verb order (het belooft).

If the main clause doesn't invert, why is there inversion (rommelt de vulkaan) right after Ook al?

Ook al is a peculiar conjunction. It counts as the first position of its own clause, which forces the verb to take the second position. That triggers inversion (verb before subject) right after it, giving us the verb rommelt before the subject de vulkaan.

Does het in het belooft refer back to the volcano?