The beta doesn't let current users give out invitations to their friends, so no one has spare invites to give you. That includes Mashable writers, your friends online, and any website claiming to be giving away Google Music invites.
Any person or website claiming to be "giving away" Google Music invites is lying, a fact we've just confirmed with Google representatives. Because of the way invites are handed out, they're linked to specific Google Accounts. In other words, one person can't request an invite and pass it on; the invite has to be requested and accepted by the same Google Account.
So far, we've seen all kinds of scam and spam out there around Google Music, from CPA surveys to data gathering apps that prompt you to enter personal information. We should be more surprised at the alacrity of these scam-hounds, but with every great product comes great potential for fraud. Free iPod, anybody?