I have one panel for the title and another for the game board, what is likely the best way to go about this?
Use a Card Layout so you can easily switch from the title panel to the game panel.
Your title panel should also probably have a button like "Start Game" so the user knows what to do. Then they can either click the button or press Enter.
and when you press Enter it advances to the game
To make the button the default button (so it responds to Enter) for the panel you can use:
frame.getRootPane().setDefaultButton(gameButton);
If you don't like the idea of adding a button then you will need to use Key Bindings.