If we look from the Earth, in opposite directions, at objects that are 13 billion LY away, they are 26 billion LY apart.
We are seeing them as/where they were 13 billion years ago, so they must have been 26 billion LY apart then.
Does this mean that, 13 billion years ago, the Universe was, at the very least, 26 billion LY in diameter?
To me, your assumptions in this OP are logical, “airtight” and are consistent with the laws of physics.
If the universe was significantly smaller (<1billion LY across) 13 billion years ago then something else will have to come into play to account for the inconsistency. Perhaps, expansion (although this would require space as a carrier)…perhaps, gravitational lensing, etc.
The bottom line is that the inconsistency between observation and the state of the universe 13 billion years ago cannot be explained away so easily.
This isn’t the only aspect that is difficult to account for. For instance; when we think of expansion; one description that comes about is that all points (particles) in our current universe were once at the center and that therefore all points (particles) in the universe continue to be “at the center”. Not hardly…of course there’s a physical “edge” and it’s no longer in the center. Perhaps the (particle distribution) edge was once in the center but it isn’t right now. If the Milky Way happened to be near the edge of the universe one wouldn’t expect the universe to look the same omni-directionally…not without extreme gravitational lensing.
No, there’s much more to understand about our universe on a macroscopic scale and expansion alone isn’t going to get it done.
