So if one can't see the distribution of this coin how do we know there wasn't a giant premine or some way for the devs to just "counterfeit" coins en masse?

These are two different things. By distribution, we mean how are coins distributed across addresses. That's relatively meaningless with stealth addressing implemented.
But there is still a blockchain so you can check the blocks yourself to see when the chain started and how many coins the blocks produced. This is no different from Bitcoin or any Bitcoin clone.
I am baffled by the complete lack of instructions for the software associated with this coin. Can someone put some instructions on how to get started with the wallet and mining? I am sure there is something within one of these 80+ pages but do we all have to reinvent the wheel?
OK, I ate my own words after looking at monero.cc.
It was linked under "Getting Started" in the OP.