Well, I think the key
word in your question is "start". Since we tend to learn things best by applying them to something of our own creation, why not start a game now, and use it as a learning tool? Obviously at first your game isn't going to do much, but as you learn new techniques in
Java you can incorporate them into your game. I'm assuming that you'll be working through a book on Java game development, such as
Killer Game Programming in Java. Before you can dive into that you will need to know the core features of Java, but presumably you are already working toward that. Looking at a book on game programming will also give you a heads-up on just what features of Java you'll need to have mastered before you can start in earnest.
If you are totally new to game design, you might want to start by looking at a non-programming game development environment like
Game Maker. That won't help you with the Java aspects at all, but it will get you thinking in terms of the types of event-handling you will need to do, aspects of good game design, etc.