Dogs do wake up early, what you should remember is that although we can go through a whole night without needing the toilet a dog has a much smaller stomach therefore needing to go to the toilet much sooner.
also do you know anything about the previous owners they may have been early risers therefore the dog being in that routine of toileting and having breakfast,
What you could try is taking your dog on a long walk to completly tier the dog out as late as you feel combfortable with doing and letting your dog out literally just before you go to bed to relieve itself.
i hope this helps please keep me informed how it all goes.
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