From the perspective of an observer comoving with the cosmic microwave background. That’s the oldest age that the universe could possibly be. You are correct that some observers would measure the universe to be younger, however it’s important to note that almost all of the universe is very close to being comoving with the CMB, so most observers would agree that the age of the universe is close to that. You’d have to have spent a significant amount of time very close to a massive object like a black hole or moving at very close to c do disagree, and there just aren’t that many places or things in the universe that fit that criteria.
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