There's no opportunity to meet people at your new apartment complex that's better than the week you move in. This is the time when you should really put your best social self forward if you are interested in establishing neighborly friendships within your new community.
After a week or two, it will be awkward to suddenly introduce yourself to the neighbor you've been ignoring at the mailbox or have passed a couple times while walking to the parking lot. So get started on the right foot. All you really need to say is "Hi! I’m so-and-so. I just moved in here."
And if you can't do that, there is always Neighborly Friends, to help get you started!! :)