A mathematically fair (envy-free) initial distribution doesn't exist as far as I know, therefore we have to get rid of the idea of an initial distribution. And switch to a permanent distribution, where everyone get's at all time as many bitcoins as the work he / she (his /her computer) performs.
Unlike the Fed, you cannot print the money without doing the work.
Which is exactly what mining is, and why mining works. People mining for the longest period of time, have the most bitcoins. People mining shorter periods of time, have less.
It's already "envy free" in that way. You can be upset you didn't find out about it until now, but you cannot argue that you haven't been mining as long as they have.
There is no way to distribute coins "where everyone get's at all time as many bitcoins as the work he/she (his/her computer) performs", because you cannot predict how much work that is, so you cannot predict how many coins to provide.
The current system is just fine.
Oh, and we're not "print[ing] the money without doing the work", people are sinking thousands of dollars, lots of electricity, and their personal time into mining. That's the definition of "work".