Okinawa was invaded by the US on April 1st 1945. We have been there ever since. I have NO idea when your dime was minted but Roosevelt's were first minted in 1946. So mercs had to be circulated or carried when the island was invaded.
Just because a park is new doesn't mean the dirt wasn't moved and before it was a park the dime was there but too deep for a detector to find. The dirt in the park also could have been brought in from somewhere else.
My guess is you found a coin that a soldier lost, in battle or right after the war.
When I was there, I used to ride my bike down the hill on Kadina to the beach. I found bullets that were imbeded in the coral along with buckles. A somber reminder of a very fierce battle that was fought there.
Get certified diving while you are there if you like water. The rule was that any WW2 stuff that was deeper than wading water at low tide was to be left there.
We found hand grenades, ammo all fused together from ammo boxes that were sunk and the box rotted away. A depth charge, naval shells that were huge, mortars and lots of other WW2 artifacts. The water is absolutely beautiful.