I haven't reviewed the original Bitcoin 0.1 code, however...
https://bitcoin.org/bitcoin.pdf
Based on the white paper Nakamoto released, "genius" levels of crypto were absolutely not required. An intelligent recent undergraduate or graduate who studied crypto could understand, suggest, and implement all of the crypto primitives and ideas discussed in the paper if they were given the scenario ("implement a distributed form of currency, with the ability to send payments and use computing power to mine transaction blocks"). No new cryptographic algorithms were invented by Nakamoto whatsoever, and his use of all the algorithms he chose have been in standard use for decades.
If you read the whole paper, you can see that any decently knowledgable CS student could grasp most, if not all of it, on the first read through. Hell, the most advanced math in the whole paper is just a handful of simple probability calculations.
Regarding C++: he's certainly a good C++ programmer, but if I recall many early contributors found his code to be messy and not that refined. It did the job and implemented the protocol, but I believe they ended up rewriting it almost from scratch later on.
The innovation in Bitcoin is the core idea and promoting the network; technically, it is not particularly innovative or unusual. Even the idea itself has been suggested by numerous cryptographers in the past decade, but only with toy implementations.
I personally posit that Nakamoto is not even a professional cryptographer, let alone a "world-class expert" or "genius". He probably has a bachelor's and possibly a master's in Computer Science. He probably worked as a C++ developer for many years and worked on some projects that involved crypto, and eventually came upon the idea of Bitcoin due to his libertarian ideals.
Going by his posting style and his actions in general, I think he was and likely still is a pretty ordinary, geeky programmer; not an academic. I think he's probably fairly young, too (under 40, maybe under 30). In fact, I think he falls right into HN's demographic.