Let's assume that our universe popped into existence with a perfectly fine-tuned set of cosmic constants to permit life. You have two options here:
1) Either that the universe was designed & fine-tuned knowingly
2) It happened randomly out of a sample of billions if not an infinite number of universes out there.
#2 is problematic. Not only can you not prove the existence of other universes - rendering such a notion as non-scientific - and therefore, as mere fiction - but also this multiverse model will be in vain if it turns out that the mechanism that generates the multiverse in the first place must also be fine-tuned, for then one has only kicked the problem upstairs.
And, indeed, that does seem to be the case. The most popular candidate for the multiverse fictitious theory is the inflationary multiverse, as it appears to require fine-tuning. For example, M-theory, the theory which supposedly governs the multiverse, works only if there are exactly eleven dimensions—but it does nothing to explain why precisely that number of dimensions should exist. There will never be an answer.
So when someone brings out the multiverse thing, just ask them: isn’t the multiverse itself describable by specific physical laws? Don’t those laws themselves include constants and boundary conditions which must be fine-tuned in order for the multiverse to exist in the first place? Rinse & repeat forever.