Nick Szabo comes 2011 with a alternative proof system wich he calls proof of stake POS. This system was used later by varios coins ( NXT, Peercoin, Blackcoin etc.) but all of them had the genesis coins premined or have them created in the beginning with the proof of work system. But how it would be possible to create coins only with the proof of stake system from the beginning ?
The problem you are describing is: how do you mine coins in proof of stake if you have no stake? In essence; you can't, depending on the implementation obviously. If you don't have any coins, you won't be able to mine new blocks. The easiest solution is obviously buying coins from another. If the original creator(s) of a PoS coin simply sell most of their early work, others could start mining as early as the third block (genesis block to finance the creator, second block to transact to others).