How can theory and ability made the field of physical cosmology possible?
This is absolutely possible. Perhaps you're misinterpreting the world 'field'. Here it means 'subject', 'study' or 'exploration'. For example, the invention of the microscope made the field of microbiology possible. Or the theory of evolution made the field of evolutionary biology possible.
This sentence looks awkward using either "because of" or "by".
That's absolutely the intention of the writer. It looks awkward but it turns out to be grammatically correct and logical. That's what makes for a tricky SC problem.
Note that we have a simple passive construction "...was made...by...". To give another example, I could say 'A thief stole my bicycle.' (active) or I could say 'My bicycle was stolen by a thief.' (passive - still fine). But I couldn't say 'My bicycle was stolen because of a thief.'