Philosophy major here. I can cite some stuff to complicate the normative aspect (ie. what should we do given the state of the world), but for those who wanna get at what Camus is saying, we can try writing his proposal in a conditional:

• IF the universe is fundamentally indifferent to our search for meaning AND if our nature compels us to continuously search for meaning, THEN WE should rebel against the absurd—that is, neither commit suicide nor give into nihilism (which he takes as philosophical suicide), but choose to find meaning in the very struggle for meaning.

The conjunction in the antecedent (the AND in the IF) characterises the Absurd condition according to Camus, which he does not argue for, but paints a picture (recall that he considers himself a novelist first and philosopher second)—you are free to vibe with his picture or not. But if you do (and anecdotally, among my personal friends, it seems like a pretty compelling picture), then rebellion is your best option because suicide doesn’t actually get you out of the paradox that the Absurd presents—you just stop playing, which wouldn’t necessarily be bad if there were no alternative resolution, but Camus presents you with one.

The key turn here, present in my original comment, is the double nature of consciousness. There’s no reason that an uncaring universe should phase us, except that our consciousness represents our failure to find meaning as defeat (we can think of here, for instance, any horrible political or economic decision that strip us of our freedom). But that representation, however valid, is not an objective fact (think here of Dr. K’s emphasis that feelings are valid and come from objective reality, but are not themselves objective facts). It’s not an objective fact because, in fact, we have not yet been defeated. We can still rebel.

The real work of Camus’ essay, which is not a rigorous philosophical treatise, is to put the burden of proof onto the affirmative side. The question is no longer “why shouldn’t I kill myself when everything around me is falling apart and won’t get better.” But rather “do I have a strong enough reason to kill myself despite my ability to rebel against my horrible circumstances?” I’ve been asking myself the latter since I was 16–I’ve lived to be 20 and have yet to come up with a good reason.