Well, the jar of anti-freckle cream is a good place to start. But Amelia wasn't the only woman in the world to use it. Then again, how many women were ever on a totally unihabited island that used that cream?
If it was a crash landing, there MUST be parts of that Lockheed SOMEWHERE. Most likely they made a water landing (no airfields on an uninhabited island) and what's left of the non-aluminum parts would be well under water -- hopefully not washed away from tides, currents and storms.
This is a very interesting mystery. Plus, if she and Noonan did land in the surf and they were able to salvage some survival gear (though I don't know if anti-freckle cream would work for sun burn protection) there has to be some evidence of building a shelter, campfires, latrine pit, etc. as well as parts of the plane.
But then, how does this tie into a photo of Amelia that was found on the body of a Japanese soldier during WW II?
If they died on that island, where are the bodies? Did they get washed away by high tides? If so, why did the shards of that jar remain?
It's like a mystery game some people play when presented with vague clues. Such as, here is a body of a person that died of a gunshot wound. There is an exit hole, but no entry hole of the bullet. Then it's turned over to the other game players to write up a solution to the puzzle and the most logical one wins the next beer.