Radius of the observable universe is 47.5 billion light years,which means we are seeing things which are about 48 billion light years away. At a rough estimate,at what distance would our finest instruments and telescopes be unable to see or detect anything at all,& is there anything in the idea that if we were able to see far enough,we might see our own galaxy as it appears from an immense distance,its light having circled the universe? And as space is not a perfect vacuum,wouldn't the light be significantly retarded by the end of such a long journey?
The furthest we can "see" is the cosmic microwave background at a redshift of about 1100.
The proper distance of the CMB-emitting gas that we see today is about 46 billion light years.
If you are talking about galaxies, then the first are thought to have formed at redshifts of about 20 (current distance 36 billion light years) and beyond that are the universe's "dark ages" where no stars or galaxies should exist; the most distant galaxies observed at the moment are at redshifts of about 10 (current distance 31 billion light years).
- All current distances depend on the adopted cosmological model. The numbers are for a flat $\Lambda$CDM universe with the Planck cosmological parameters.
There is no chance of seeing our own Galaxy, since it only formed about 12 billion years ago and the universe is a lot bigger than 12 billion light years.