Are you contending that if man has yet to devise a test for certain potential explanations for phenomenon that said explanation can not be possible?
Whether an explanation is possible or not is hardly the question. The question is what sorts of explanations we can test and which ones we cannot. Mechanistic explanations are testable, at least in theory. Teleological explanations are not testable, even in theory. ID is a completely teleological explanation, it does not attempt to explain mechanics, as its proponents are quick to point out. This means whether it is true or not is quite besides the point. As Judge Jones pointed out in his Dover decision, ID may be true, but it is not science.
Now, back to your abiogenesis query, let's unpack the only question that matters. We know that organic molecules like amino acids and nucleic acids can form spontaneously, and we know that simple life forms are found in the early history of life (but no complex ones). What we have is a gap between the simple organic molecules and the simplest known life forms. This gap can be filled in a couple of ways:
1) The "designer" intervened directly, i.e. God or aliens if you prefer
2) Some sort of vitalist substance, as yet undiscovered, bridged the gap
3) Naturally occurring, self organizing processes of chemistry and physics
We do not _know_ for certain which of these explanations is true. What we do know is that for every phenomenon we have discovered to this point, a natural, mechanistic explanation has been found. Given the weight of the evidence in favor of natural, mechanistic explanations, it would seem that the third explanation is more likely than the others to be correct based on current knowledge.
So the question is not if we know the answer, the question is which is more likely. So, which one do you think is more likely and why? (if you have a different candidate explanation, I'd like to hear that as well)
Note I am not asking if you _know_ the answer, I am asking which of the available possible answers you think is most likely to be correct and why.