Or then a thousand specialists did that, and Cochrane just jumped in at a convenient point.
The man is credited with "discovering the space warp", and since we can now tell he didn't discover it by stumbling into it like one would discover, say, the Americas, we must assume he either figured out the theory behind the phenomenon, or then stumbled onto the phenomenon in some lab, and then proceeded to write some papers.
Whether he then also built scale models and the like, or had the job assigned to Boeing while USAF kept him in an office writing more papers, we don't know - that stage of his life is behind him for good in ST:FC. Whether he built any part of the Phoenix is also debatable - it's actually Sloan who claims to have been involved in the building, not Cochrane.
Really, we can vary a large number of parameters for a variety of scenarios, from a meek US government worker to a criminal mastermind, from a drunken test pilot getting fortutiously misidentified to a brilliant scientist getting forced into the dirty life of a zombie hunter cum spacecraft hobby builder.
In most of those scenarios, he'd have access to stuff allowing him to land all of the Phoenix more or less safely, even if one piece at a time. We have enough pointers that the hardware should not be difficult to come by at that time and age.
Timo Saloniemi