Taking as granted it is not your connection or that you could have some technical issue:
a) Verify the Game Integrity: Via Steam, right-click on Conan Exiles and choose Properties. Go to the Local Files tab and click the bottom option ‘Verify…’ This will take a while. Go make something to drink and be patient.
b) Go into Conan Exiles and go into a Solo game. If all works okay, then you know thtat the game works.
c) Exit the game and go back in and this time choose Online. I would choose a completely different Server, in your area and without mods and go in there.
That should work If you know any players on the server you are usually on, check if they can get in. (easy to see: is anyone showing in that server)