To expand a bit on Kim_123’s answer, because I have the feeling that the second aspect of your question is not yet covered, namely whether you have to start a search for every county.
You can use "Map compare" to (more or less) solve this problem. If you want to see the oldest caches for all counties in e.g. Belgium, select Belgium as country but nothing in the fields for state or county. Select, as appropriate, the options "none found"/"one found" and "show disabled/archived".
What you get is a list of all caches, sorted for the counties. (In Belgium PGC uses the municipalities as "counties", so we have a lot.) You see this in the list under "Location". It starts for each "county" with the lowest GC-code, which is likely to be the oldest cache in that municipality. (If in doubt, you'd have to look at the cache pages, though, to see when it was actually hidden/published.)
One caveat: because of the limit of 10.000 caches, which also Kim_123 mentioned, in bigger countries you would have to select a "hidden to ..." filter. Of course, if the oldest cache in a county is rather young (i. e. younger than the filter) the entire "county" will not show in the list. So, it’s not a 100% solution but maybe it helps.
As an example the link for Belgium (with a filter up to end of 2008): https://project-gc.com/Tools/MapCompare?profile_name=Beetstar&country=Belgium&nonefound=on&onefound=on&hidden_toyyyy=2008&hidden_tomm=12&hidden_todd=31&submit=Filter