Clearing the substrate for an inlay

I working on finishing my grandson’s crib. The end panels are going to have an inlay like this…

As you can see, there is a lot of real estate to clear out. I have been avoiding this because I am uncertain as to how to proceed. When I make space on the end panel substrate (3/8 ply with maple veneer) for the inlays, should I clear from the center out, or from the edges in?

I am nervous about not having enough support surface for the router.

-- There are three kinds of people... those who can count, and those who can't