They probably buy the initial capital from somewhere like how we do when we are willing to start a business investing bitcoins in it, and when they are done with that and they started their exchange, they just earn bitcoins from the fees of transactions and trades, like in yobit they charge you 0.2% from every trade you make, and also they charge some fees on withdrawals as well, so that is how they earn their bitcoins.
Yes I think so, the Bitcoin from fees of transaction and and trade is seems small, but if so mnay people do yransaction the exchange site will get realy big profit. I think in the first launch of the exchange site, the Developer need to prepare the financial capital. then if the customer do transaction and get profit from fee, they can increase their financial to fulfil buy order. That is my oppinion, I also think that probably the customer of exchange can buy bitcoin if only other customer sell their bitcoin, this reason is most logic.