Meet your neighbors.
There are exceptions to this rule: if Gregorian chants blast at all hours or you can hear an army of ferrets scuttling around it might be best to leave them alone. But you have a lovely, skilled property manager — you signed with her, right? — so we're willing to bet the neighbors are nice people.
It's never too early. Knock on move in day; introduce yourself, perhaps the cat. Remind them that if they need anything you're a few feet away.
It's that simple. It'll work to your advantage when you need someone to, say, pick up a package. And when your neighbor gets a case of good beer one might come your way.
Say hello and do unto others. Common sense, perhaps, but worth repeating.