Isn't the universe older than 13.8 billion years? To preface this, I'm not an expert, I'm just an avid astronomer with little mathematical knowledge.
I was watching a video that was explaining the cosmic scale and how the observable universe is only a fraction of the whole since the light from objects passed the cosmic horizon haven't reached us yet and it got me thinking about how we know the universe is 13.8 billion years old.
If we found the age of the universe based on redshifts and how long it takes the light from objects at the edge of the observable universe to reach us, would the age of the universe change if we stood at the cosmic horizon and measured the light of objects further out since we'd have expanded the boundary of what we can observe?
Let me try and word it differently. If the radius of the observable universe is 46 billion light years from earth and we stood on a planet 46 billion light years away and used the Hubble telescope to see another 46 billion light years, would we have to recalculate the age of the universe since we'd be looking at objects in a radius of 92 billion light years?
 A: 
If the radius of the observable universe is 46 billion light years from earth and we stood on a planet 46 billion light years away and used the Hubble telescope to see another 46 billion light years, would we have to recalculate the age of the universe since we'd be looking at objects in a radius of 92 billion light years?

You can have an age of 13.8 billion years and an observable universe of radius 92 billion light years. This is because the universe expands. If it expands fast enough then you can have an observable universe that seemingly expanded faster than the speed of light - which doesn't break relativity, because nothing physical is travelling faster than light. See e.g. this Forbes article for more details.
By extension, the size of the observable universe does not matter when calculating the age of the universe, because it all depends on how fast the universe expanded in the past. If the universe ever collapses in a Big Crunch, just before the singularity, it would be tiny, and also much older than 13.8 billion years.
A: 
If the radius of the observable universe is 46 billion light years from earth and we stood on a planet 46 billion light years away and used the Hubble telescope to see another 46 billion light years, would we have to recalculate the age of the universe since we'd be looking at objects in a radius of 92 billion light years?

If the universe was 92 billion years old, the observable universe would be everything within 92 billion lightyears (once you account for expansion of course).
If you go to the edge of the observable universe, you're no longer looking around at objects 13.8 billion years old. Even if you teleported there, you'd get there 13.8 billion years after the light we're observing from it right now.
