' ... limitations in physics, ... the finiteness of the speed of light ... '
' ... this also means that we can observe the universe at different epochs (..) thus tracking and reconstructing cosmic history...'
The speed of light isn't even a velocity but just a number which says how many meters correspond to how many seconds, so you can never travel a greater spacedistance than the timedistance it corresponds to. Like some rulers which show lengths in centimeter at one side and in inches on the other, their ratio being 2.54, nature's ruler has a length scale at one side and a time scale at the other, the ratio between meters and seconds being c. Spacetime is not a space where it is everywhere the same time: the idea of a universal clock, which comes down to a clock outside the universe directing the pace of all events inside is a truly religious notion. As it isn't everywhere the same time but clock readings depend on the observer and the observed process, as there's no point in the universe from which unambiguously can be determined where it is earlier or later, a photon cannot even know in which direction it moves (in its confusion destroying causality). Only an object interacting with the environment it travels through can have a velocity with respect to the things it interacts with: as the photon cannot express its existence in interactions with the environment it is supposed to travel through, the part "with respect to" doesn't even apply, so the speed of light is not a velocity.
As it took me years to accept this and only now am beginning to understand this dichotomy, its need in nature for engineering purposes, I suspect this to be hard to fathom to the reader: that Newton was right in thinking that light is transmitted instantaneously, and Einstein in equating a spacedistance with a timedistance, but, unfortunately, confusing a timedistance with a duration. As to a photon the world it travels in doesn't exist as at that speed it cannot interact, express its energy as gravity (interactions which would affect its velocity and presuppose the existence of influences propagating even faster), to the photon there is no space- nor timedistance between its emission and absorption, its transmission is instantaneous, notwithstanding the fact that an observer measures a time proportional to the distance between the points it is transmitted as to him they have different spacetime coordinates.
That said, you can move much faster than 300,000 km per second, if, as you should, calculate the distance to your destination when at rest, but divide this by the time the voyage took according to your watch, but you'll never be as fast as light as its transmission is instantaneous. It is only with respect to someone along your path that you can never cross a spacedistance larger than the timedistance it corresponds to. Though this means that we indeed do see our whole universe, as we cannot receive photons of an energy which is less indefinite than the position of its source (see Mechanics of a Self-Creating Universe), a position which is increasingly indefinite at increasing distances, we see galaxies in longer wavelengths, in an earlier phase at larger distances, though this definitely does not mean that we see them as they were in the past. It is because we believe in the Big Bang nonsense that we assume that all galaxies are about the same age, as if there is a universal time, a clock outside the universe which determines the pace of all events inside, the universe like a huge clockwork mechanism which, once winded, only can run down. The job Copernicus started is far from finished : after acknowledging that every point is at the center of its own universe, part two is to finally admit that as there's no clock outside the universe, no point from which unambiguously can be determined what precedes what, the concept of causality has become useless in physics.