How come there's light from places millions of light years away reaching us now?
There are several theories for that, most of which really suck.
The best might be White Hole Cosmology. I read a book on that 7 years ago, but may not remember it all right and I hadn't taken Calculus yet so I couldn't really even attempt to check most of its equations.
It can be derived from General Relativity if you reverse a couple common assumptions astronomers make.
First, you have to assume that matter in the universe is bounded, concentrated to a central area in space rather than roughly evenly dispersed throughout. This makes it so that the universe has a center of gravity, and thus significant gravitational time dilation. The universe could be trillions of yeas old in Swartzenchild time (that is, at a point measured from far enough away for time dilation to be nil) while being only a few thousand years old when measured in local time at the core.
Second, you must reverse the "Copernican Principle," that is assert that Earth is at (or rather very near) the center of the universe.
Apparently the assumption that the universe is unbounded and has no center is mostly for the sake of simplifying calculations; without a center any point in space can serve equally well as the origin in mathematical models, whereas if there is a center it must be used as the origin or else complex transformations are needed to mitigate errors that would grow increasingly the further the assumed origin is from the center of the universe. IIrc actually proving whether the universe has a center or not would be possibly only if we could make and compare accurate measurements from hundreds of light years apart.
A bounded universe would apparently have too either be collapsing into a blackhole or exploding out from a white hole. The white hole option is actually closer to the popular conception of the big bang than the real scientific theory is, but still depends on space expanding. IIrc the model requires a changing "Cosmological Constant," representing the 4D analog of pressure applied to a 2D surface and thus is a sort of force originating outside of our space time continuum. I've read there are some observations that seem to imply that this yet unmeasured "constant" actually does change.
I saw an article maybe 5 years ago by the same author of the book that reworked a few sections, saying that after he worked our the formulas himself rather than trying to run some of Stephen Hawkin's black hole equations in reverse he found that there are some really odd things happening near the event horizon of the white hole, and that in one region within time is not only slowed but stopped.
One other thing I recall from the book is that Red Shifting actually depends on the expansion of the space through which light travels and not on the distance or time it took to travel through it. The rate at which the space may expand during that time is essentially unlimited and unmeasurable. It seems Hubble's Law can accurately determine the distance to a point in terms of how long it would take light to travel through space without it continuing to expand but we can say nothing of how much time it took to make the trip without making a fairly arbitrary assumptions on how space was expanding in transit.