In other words: we can’t look at the entire universe, we’re not omniscient. How can we say, for sure, that something doesn’t exist in the whole universe, without using a degree of faith — that is, belief without evidence to support it?
Well, it depends, in a way, on what you mean by “no god”: not that god, or no god at all?
It’s very likely that, by “god”, you mean the Judeo-Christian god, Yahweh, as described in the Bible. If so, I can answer that one easily: do you need faith to say Odin doesn’t exist?
I’m sure that you don’t. You have no reason to believe in Odin, no evidence of his existence. Besides, Odin and all the other Norse gods are clearly anthropomorphic; that is, they’re exactly like humans, only “bigger”, more powerful. But with the same emotions, traits, character flaws, of humans. It’s safe to say that he’s made up by ancient Norsemen.
Well, all of that applies cleanly to your god, too! That’s why one doesn’t need any “faith” to say that he’s been invented by men, because there’s a lot of evidence in that direction, and exactly zero in the opposite one.
Besides, there are many logical arguments against the existence of an entity such as the Judeo-Christian god. Take the omnipotence paradox, or the problem of evil. The former is logically self-contradictory; the latter requires such convulted excuses (follow the link, they’re all examined in detail there) that it soon gets ridiculous.
But maybe you didn’t mean a god like that. Maybe you’re talking about a vast, cosmic being, who didn’t create the universe, but who is the universe. A being who, because it wasn’t invented by men, doesn’t have human traits; who isn’t focused on, or probably even aware of, our insignificant little planet, who isn’t concerned with trivialities (in the cosmic sense) such as “prayer”, “sin”, or “the afterlife”.
As suggested here, such a being, if it existed, would be completely undetectable by us, would not in any way interfere in our lives, or be concerned with us at all. In every possible sense, it is as if it wasn’t there; nothing we could do would affect it in any way. Much like the “do we live in a perfect computer simulation” questions, it is most likely impossible to know, and ultimately irrelevant to our lives (though there’s nothing wrong with being curious).
In both of the above cases, there’s also something definitive against the “you need faith to say it doesn’t exist” position: burden of proof. It’s always on the side of whoever claims something exists, and it’s him who has to provide evidence for that existence. If he doesn’t, the logical position is to say that his claim is false, and no “faith” is required for that.