Is the universe contingent?

This morning I came up with an argument for the contingency of the universe, but I don't think it's a sound argument. I'll tell you what the argument is, then tell you why I don't think it's sound. Then I want to know what you think.

This argument came to me as I was having a conversation in my head, so I'm going to give it to you in the conversational way it happened.

Jim: Is it possible that another universe exists?

Bob: Yes.

Jim: Is it possible that another universe does not exist?

Bob: Yes.

Jim: If the other universe did exist, it would be contingent, wouldn't it?

Bob: Why?

Jim: Because we've already said it's possible for it to not exist.

Bob: Yes.

Jim: If the other universe is contingent, then this universe is also contingent, isn't it?

Bob: Why?

Jim: Because they are of the same kind of being--both universes.

I think the problem with this argument is that it equivocates on what it means to be possible. Something can be possible in the epistemological sense but not in the ontological sense.

Consider a person who does not understand geometry. This person might think it's possible that the interior angles of a Euclidean triangle do not add up to 180 degrees, but ontologically, that is not possible. It's only possible as far as he knows. So it's an epistemological possibility, not an ontological possibility.

In the same way, the non-existence of another universe may be possible for all we know, but if it's a necessary universe (unbeknownst to us), then it's not possible for it to not exist ontologically speaking.

I guess you just have to be careful in arguments like these not to equivocate. Equivocation is a fallacy, but we don't always commit this fallacy on purpose.

What do you think?