I know that before the beginning of the 20th century it was thought that the Milky Way galaxy was the whole universe. Then there was the discovery of galaxy redshift, and the size of the Universe was considered to be much larger. But who was the person or persons who arrived at the figure of 46 billion ly (proper distance)? What year was it?
There was no single person who discovered the current estimate of the radius of the observable universe, nor was it discovered at one particular moment in history.
A primitive version of the big bang model was first proposed in 1927 by Georges Lemaître. Early observational work that helped to build up the model was done by Vesto Slipher, Henrietta Swan Leavitt, and Edwin Hubble. The first mathematical models of big bang cosmology were the Friedmann–Lemaître–Robertson–Walker models, created in the 1920s and 30s.
These models describe the big bang as the beginning of time itself, and that immediately implies that since light has only had a finite time to travel, the observable universe has a finite radius. Although this may seem conceptually straightforward, keep in mind that there were competing models such as the steady state model, which were taken seriously as late as the 1960s.
Roughly speaking, the radius of the observable universe is on the same order of magnitude as the inverse of the Hubble constant. The Hubble constant was first estimated by Hubble and others around the 1920s and 30s, but the estimates were extremely rough. Its accuracy was gradually improved over the decades.
To get the modern figure of about 46 billion light years for the radius of the observable universe, you need an accurate cosmological model of the past expansion of the universe. That requires knowledge of the acceleration of cosmological expansion and dark energy, which came from a number of different workers, using several independent methods, starting around 1998. That work is still going on.