Assuming physicalism is the case and not idealism, dualism, or some other metaphysics. If consciousness isn't the result of neuronal activity, then that would be a good reason to suspect that physicalism is somehow false.
To be pragmatic - the absence of a physical cause for consciousness does not preclude any other causes. Whatever environment consciousness exists in that environment must have rules, laws, constants, and symmetries that define that environment. So all we're doing is trading the laws of the universe for the laws of some ethereal no-material realm or supernatural realm. We're not actually performing any useful work, we're just shuffling the problem around.
The hard problem of consciousness, the questions of determinism and free will - these problems will challenge any consciousness that finds itself in a rule-bound system.
If falling isn't the result of gravity, then that would be a good reason to suspect that physics is somehow false.
If it's not neurons, you're going to need extraordinary evidence!
I'm not saying it's impossible. Who knows. But it remains a hard problem for now, at least.