How to approach research on an unproven theory for academic submission? I'd like to look more into the Fermi Paradox for research purposes and possibly submit it as an academic paper. 

The Fermi Paradox is a theory proposed by a scientist that has some very interesting and factual points based on our current knowledge of space and technology advancements. 

My only concerns are the entire theory is based on speculation while it's not possible to disprove it's also not possible to prove. 

Is it acceptable to research from one stand point either against or for the theory. Or is it better to approach it from a non bias stand point and show the evidence and the possible counter evidence?
Lots of interesting things in science are not proven, so I don't think there's any special privilege for unproven theories vs. other types of subject.  The real question is this: what do you have to contribute to the intellectual discussion? It doesn't really matter whether you start from a perspective of aiming to prove, aiming to disprove, or just aiming to clarify (in fact, you might well change your perspective multiple times during your investigations). What really matters is that you will need to gather novel evidence that advances the state of knowledge with regards to the subject.