In reality unless you are already heavily involved with an Olympic sport you have bugger all chance of winning a medal
90% of Olympians don't win a medal, so maybe set your sites to just become an Olympian.
Find a sport you where you can get to a standard to meet the Olympic qualifying standard, identify some long lost lineage from a country which has a particularly weak team or who are open to bribes.
Change nationality to said new country, pay said bribe, book in for your Olympic tattoo, simples

Perhaps clay target shooting, not as difficult as air rifles or archery because you have pattern of pellets and you only have to break the clay in two to have succeeded.
See you all in Brisbane