Assuming the Big Bang was 13.8 Billion Years ago: Is it possible to observe a Galaxy's redshift showing distances slightly greater than that, like 48 Billion Light Years away? I understand that in a static universe, light traveling in a straight line would only be visible at less than 46.6 Bly. But, can Hubble's constant distort this number? Also, do we assume some error due to the light taking a non-linear path because of lensing? If so, is it possible to have an error of several hundred million years?
The edge of the observable universe is actually 46.6 billion light years away, despite the Big Bang being only 13.8 Billion years ago. This is because the light which we are now receiving as the furthest visible stuff had to travel through ever expanding space in between, being redshifted down into what we call the Cosmic Microwave Background Radiation (CMBR). There is a little bit further than that which we are technically receiving, but it has been redshifted infinitely.
To see anything further away than 46.6 Bly, it would have had to existed literally before time itself, or travelled faster than the speed of light. Two highly improbable things
No that would be impossible. Even if we were to observe a galaxy that is basically infinitely redshifted it would not be interpreted as having its light sent out earlier than 13.72 billion years ago or now being more than 47 billion light years away. This is because of how the formula for how to calculate distance from redshift is designed.
Answer: No matter how redshifted a galaxy we find, it will never, using our current model, be interpreted to be more than 47 billion light years away.