Are we seen or not by an observer from a galaxy farther away than the age of our solar system?

Question

I looked at this question.  There's one answer that alludes to what I'm asking, but I don't find it satisfactory, because to me the following is still a paradox:
The most distant galaxies we have ever observed appear to be around 13 billion light years away.  Here's my question:  Suppose the universe were not expanding, and suppose an observer in a galaxy 10 billion light-years away from us RIGHT NOW were to look directly at our planet (or rather at least the section of space our planet is occupying) with some magical telescope powerful enough to do such a thing.  In this hypothetical scenario, both our planet and this galaxy would be static.  The physical distance between the two doesn't change throughout all time.  If we can observe such a far away galaxy (albeit as it was 10 billion years ago), could an observer in this supposed galaxy see earth?  You'd say no, because light from our earth hasn't had enough time to reach the galaxy, with Earth being only 4.5 billion years old.  But how is it that we could see such a galaxy from our viewpoint?  Agreed that when light left that galaxy the earth was still a twinkle in the Milky Way's eye.  But the light made the distance.  At the same instant the distant observer looks at us and finds nothing?
Why is it that we can see them and they can't see us?  Again, static environment.  Light works one-way only?
What are the conditions for simultaneous mutual observation??

Emmy · Accepted Answer

You should take care when talking about a "now" on large distances. In special relativity, there is no such thing as a "now" which would be the same here and at a distant point; and you could hit at paradoxes if you stick to that idea (see here).
The best thing you can do is to think in terms of past and future light cones. The past light cone of an event $E$ in spacetime (an "event" being combination of a time and a position) is the set of all other events from which $E$ can receive a light signal. The future light cone of $E$ is the set of all other events to which $E$ can send a light signal. The event $E$ can only be influenced by events located inside his past light cone, and it can only influence events located inside his future light cone. We talk about it as the causal structure of spacetime.
Now, going back to your galaxies : there is nothing wrong once you drop the idea of "simultaneous mutual observation". Your far away galaxy should be inside our past light cone for us to observe it. But may there be observers out there, earth could not have entered their past light cone yet (a little drawing is incoming).
Here it is :

Adrian Howard · Answer

Because, not accounting for the expansion of space, we are seeing what was in their galaxy 10 billion years ago if they are 10 billion light years away, we do not know what it looks like right now. If observers there are looking towards our part of space right now they will see what was here 10 billion light years ago, most likely the molecular cloud that we were formed from since our Sun is only about 4.6 billion years old. So, at this moment, we would both see only each others past.

Answered by Adrian Howard on January 26, 2021

Kristoffer Sjöö · Answer

If we and they are looking in each other's direction right now, they won't see us because we weren't here 10 billion years ago, and we won't see them because they weren't there 10 billion years ago.
Perfectly symmetrical situation.

Are we seen or not by an observer from a galaxy farther away than the age of our solar system?

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