Why would it be possible to even gauge the likelihood or unlikelihood of the existence of such (a) being/force/existence(s)? And were it possible to gauge, what point would that probability have? No, this is not a sensible line of inquiry. What one should instead seek to determine is IF it is possible for the universe to exists as it does with such a supernatural dimension, as well as without.
If it is possible that the universe's known state(s) could feasibly exist without the existence of a supernatural dimension, there is nothing to prevent the non-existence of that supernatural dimension (i.e. it is POSSIBLE that supernatural things do not exist). It is not however possible to take this one step further, to prove that supernatural things cannot exist - since it is possible that such a dimension might exist in such a way that no interaction with that dimension can be detected or accurately predicted. Perhaps specific supernatural claims might be disproved (depending on their specificity and falsifiability), but many supernatural claims lack this capacity and are instead unfalsifiable.
Edit: Science has developed feasible models for the existence of the universe as we know it without a supernatural dimension
If it is possible that a supernatural dimension could feasibly exist without preventing the existence of the universe in it's known state(s), there is nothing to prevent the existence of that supernatural dimension (i.e. it is POSSIBLE that supernatural things exist). It is not however possible to take this one step further, to prove that supernatural things exist - since it is possible that anything which we deem 'super'natural is merely a misunderstood part of the natural or else our senses playing tricks on us.
Edit: Religion has developed models for the existence of an unfalsfiable supernatural dimension without preventing the existence of the universe as we know it (though such models are abstract and rely on being undetectable and upredictable)
That is the limit of our capacity to inquire of the existence of the supernatural.