How do you find ancient coins? Go to Italy, Greece or anywhere in that general area. Your metal detector will do the rest. Coins over 2500 years old have been found. Oh, I forgot about China.
We only know what has already come out of the ground. I have seen metal detecting videos featuring people finding Roman gold coins. Others have found medieval and even earlier. Given that, it seems like coins from all ages remain hidden in the ground somewhere (someone already pointed out the dominant variable of location). But it's difficult to know what the oldest one is without finding it and knowing that it's the oldest. But one has to find the oldest to know it's there. But how do you know it's the oldest until someone finds an even older one? Infinite regress. I think it's fair to say that evidence exists that one can still find coins of great antiquity in the ground. But no one knows the oldest one possible nor how many of any type remain.
It might also depend on your metal detector. The older the coin is, the deeper it is likely to be, so you'll only find coins as old as your detector can find.
What is the oldest coin you can find metal detecting I think you should have substituted the "can find" with "have found" or @Inspector43 question stands as correct. LOL
Kingdom of Lydia in what is now Turkey, circa 600 BC or so. Some say Phrygia or Aegina around the same time frame.