There are plenty of invites going around. I've been on Bluesky for about a month now and have gotten half a dozen invites.
The thing that is, however, making Bluesky a genuinely pleasant place to hang out, even despite its size (it's getting relatively large for pleasantness!) is that the invite code system requires that, even with that large number of invite codes, somebody wants to see your posts. It is a pretty strong high-pass filter; they're just scarce enough to value giving them to folks who are going to make for interesting reading.