What is the crucial assumption in the example you give? It is that the examination of the room is adequate to the end of ensuring that the dog cannot escape as you close the door. Yet Penn and Teller have repeatedly done the cup and ball (walnut shells and pea) game with c
lear glasses and people still get it wrong with about 100% consistency. They are even doing a study now at a university with the central idea of the gullibility of human perception in stage magic. You see, about the only two things a human can be certain of is that they can say in truth “I am,” and that they are wrong. By “wrong” I mean that what might work for one person situationally might get another killed in their circumstances, eg protective clothing in the desert vs the arctic. Both have a “right” for the situation in terms of clothes which is not interchangeable.
As for the dog thing, it is like the Heisenberg’s cat. It may or may not be there. Even if you hear it barking, all you can say in truth is that you hear a dog barking and the sound appears to be coming from the room. Past that, even if it is “reasonable,” fundamentally, to say the same dog is in the room as you left it, is a speculation and not warranted. It’s like the monkey they put in a box that had four ways out and no more. The idea was to test the intelligence of the monkey by which way it discovered to get out. It found a fifth way. We forget, just because we have a mind, that that mind has an phenomenally narrow range of interaction with Universe even aided by instruments. And anybody will assure you that for all practical purposes their paradigm of reality is 1/1 accurate. I guess that is why there is such agreement world wide as to what is, and how things ought to work.
Further, you only have two categories: belief and non belief. There is a third, and as far as the concept of God is concerned it puts both atheism and religion in the same boat. And that is based on the study of the only two things mentioned above about what one can be certain about. It actually puts the ball of considerations relative to God in a court where it can be played usefully beyond religious affirmation or intellectual denial.
So, again, while faith is necessary and useful in a relative way as a part of engaging navigation of the world, teleologically at its extreme it resolves into having to deal with the two factors I mentioned. The first is a door, and the second a tool, maybe a doorknob. Both lead away either from faith or from atheism.