When you talked about mining bitcoins, that happens when your wallet solves enough mathematical problems to verify enough of a block/s that you can be awarded some bitcoins. This is typically not cost-effective, at least for most normal computers, as generating them is fairly slow and energy-intensive. The only alternative to get substantial amounts of bitcoins, buy buying them, can only happen if you find someone who wants to sell you bitcoins. The most reliable way is through the sites you mentioned, however if you can find some user out there who is willing to trade, say via an irc channel, or some other way, you are free to trade that way. This is less safe though, which is why it is better to stick to the trusted exchanges and marketplaces.