One can believe that a handful of Spartans held off half of the Persian empire
As the actual, historical account of the battle of Thermopylae goes, the local geography gave the Spartans a tactical advantage which allowed a much smaller but more organized force to temporarily hold off a significantly larger foe. Please avoid confusing badly made Hollywood jock-fests for real history.
yet not believe that Jesus cured the sick.
If a holyman named Jesus once lived, it is quite possible that he learned the use of herbs and other naturally occurring substances to treat most common ailments, but that's not quite what you're suggesting, is it? Magic doesn't exist, whether you call it voodoo or "divine miracle".
One can believe that Achilles was a mighty warrior yet had a weak ankle,
Not really, that is just a story from "Homer's Odyssey".
yet cannot believe that Noah had built an ark.
There isn't a single place on this planet, natural or man-made, that has ever had all the animal species. Noah would need several cargo jets and a very large team of trappers and zoologists, just to gather the animals.
One can believe Alexander the Great conquered almost the entire world in his twenties.
One shouldn't, because he didn't.
but cannot believe the Earth was created by a God.
There is historical and archeological evidence of Alexander of Macedonia, there is none, sadly for any God.
