Well, without experimental proof, where are we?
It's not even clear that we can do experiments that will definitively tell us what the early universe was like. Inflation answers a lot of questions, and gives testable predictions, which are confirmed. If inflation also implies that there is a multiverse and not a universe, it is an implication of the theory. To argue against it definitively you'd have to come up with a new theory.
Exactly, and untestable hypothesis at best. We need a grand unified theory, and then examine it for anomalies.
What type of anomalies are you referring to? Surely not the axial vector anomaly?
All we could say, is that it's not impossible for another universe with different dimensions to exist. We could not prove one does. It's a thought experiment at best. For any proof, we need some dimensional overlap, an observable ramafication in our Universe, that cannot be explained by what we know to exist here. If you think that may be inflation, that could be exciting, or we may just find something mundane to explain it. I'd prefer excitement, but somehow think it's going to be a simpler answer, if soluble at all.
If one is led to the existence of a multiverse by a string of consistency checks, we have no choice but to accept it, unless another theory comes along which better explains the data.