The universe is and has always been infinite in size. It has also existed forever in time. We'll explain these assumptions later (tl;dr: Occam's Razor). We are challenging the conventional notion that the universe had a start point in time, the Big Bang, and at that start point it was infinitesimally small.
A long time ago, the infinite universe was very hot and dense, so hot that the 4 known fundamental forces (gravity, strong, weak, EM) were merged into one.
Space expanded, so the universe got cooler. Note that space remained infinite in size as it expanded, kind of like multiplying infinity by 2. It's twice as large, but still infinity. Things close together got further apart throughout the infinite universe as it expanded.
At some time point, Tgravity, it got cool enough for gravity to separate out from that one merged fundamental force. Tgravity is a negative number for reasons we'll explain later.
Space expanded more, the universe got cooler, and at time point Tstrong, the strong nuclear force separated from the electroweak force. Actually, we'll define Tstrong to be 0 for reasons we'll explain later. So, immediately after this time 0, the forces were gravity, strong, and electroweak.
Space expanded (a lot) more, the universe got cooler, and the weak nuclear force separated from the electromagnetic force at time T_weak. We actually know the value of T_weak to be about 10^-12 seconds based on particle accelerator experiments which can recreate the temperature of the universe (slightly) before T_weak.
We wrote above that space expanded "a lot" because, during some interval between 0 and T_weak, inflation happened. It happened much closer to the 0 end. More about that later.
The unconventional selection of Tstrong=0 is motivated by philosophical and practical considerations of what we can and cannot know. There is a huge energy gap (10^12) between the electroweak and Grand Unified Theory scales: GUT explains the universe between Tgravity and 0, i.e., "negative time". We will "never" be able to do experiments at the GUT scale: certainly not on Earth. They are too unimaginably difficult: a trillion times more energy than the LHC. Therefore we will never be able to know (that is, experimentally confirm) what the universe was like at or before time 0. Incidentally, this means we will never know what time Tgravity was.
Similarly, we will never, ever, be able to experimentally confirm a Theory Of Everything (TOE), a theory about what universe was like before the negative time point Tgravity, called the Planck scale. In fact, time points before Tgravity might be ill-defined, because gravity separating out from the other forces means that only then did spacetime come to exist, so only then did time itself and consequently things like causality come to exist. Before that point, timey-wimey wibbly wobbly.
(Maybe our descendants or alien civilizations will prove me wrong about what we can scientifically know, then we will regret this choice of zero (like Fahrenheit). Scientific American's The Amateur Scientist did whimsically propose building an Ultimate Collider to test TOEs.)
Actually time might have also behaved funny during inflation: inflation did very strange things to space, so we speculate it also did strange things to spacetime and consequently time. We may never understand inflation: it is so close to the GUT scale that experiments probing it seem almost as unimaginable as experiments testing a GUT. It might have been better to define the end of inflation as the zero time point. Only then did time start flowing the way we experience it now. The quoted value of T_weak above is the time interval between the end of inflation and the end of the electroweak epoch.
Nevertheless, even though we will never know what the universe was like before time 0, we will assume that it always existed all the way out to negative infinity. (We may need some yet undefined notion of what it means to exist before time itself began to exist at Tgravity.) We assume infinite existence because it is the simplest model: Occam's Razor. If we don't assume it, then we have to explain more complicated things: what existed before the universe burst into being? Why did the universe burst into being?
Similarly, we assume that space is infinite. Currently, there is a finite patch of the universe we can see, because light has had time to reach our eyes. Astronomers call this the Observable Universe, which is kind of a confusing name. Better would have been Our Finite Patch Of The Universe. Lots of confusion stems from conflating "universe" (assumed infinite) and "observable universe" (definitely not infinite). Even though we cannot see beyond Our Finite Patch Of The Universe, we assume that the universe extends infinitely beyond it. This is again the simplest model. Otherwise we have to explain complicated things like, what does the edge of the universe look like? What exists beyond the edge?
Similarly, we also assume that space has always been infinite. At no point in time was the entire universe compressed into a point. Things were denser and closer back then, but the extent of space was always infinite. This is the simplest model: otherwise, we have to explain complicated things like, what existed outside of the finite (in fact zero-volume) point? How did the universe transition instantaneously from 0 to infinite in size?
When cosmologists say, at such and such point in time, the universe was the size of a grain of sand, it is actually confusing shorthand for, the chunk of space that eventually expanded to Our Finite Patch Of The Universe was, back then, the size of a grain of sand. It is just shorthand for the expansion factor between then and now. That sand-grain-sized chunk of space back then was still part of an infinite universe.
The conventional narrative that the universe started from an infinitesimal point at the Big Bang is derived from running the equations of General Relativity backward in time. If you do that, it does predict a singularity, and conventionally, that singularity point is defined as the zero point in time, as opposed to a later point in time Tstrong defined as zero above. However, running GR backwards all the way to the singularity is a little bit silly, because other things happen on the way to the singularity, namely some GUT, some TOE, which might interfere with the prediction of the singularity. Or, in this essay, we assume they definitely will interfere and prevent the singularity because otherwise it leaves us with the complicated questions mentioned above that we are avoiding by Occam's Razor.
Throw a ball, and we can plot a parabola, then extrapolate where the ball will land. This is analogous to extrapolating that the universe began as a singularity. However, we are actually throwing a ball toward a wall of fog. This fog corresponds to the GUT scale, time 0, that we will never have knowledge beyond. We have no idea what lies in the fog; we have no idea whether the ball will land at the extrapolation of the parabola into the fog. This essay assumes that something analogous to a bottomless pit exists inside the fog: the ball never lands; the universe has no beginning.
I suppose the more accurate analogy is we see a ball having exited from a foggy area traveling a parabolic path. From where and how was the ball launched?
In critique of this essay: because we will never be able to test a GUT or TOE, the only way to choose among them seems to be by Occam's Razor again. Are there simple such theories which permit the GR singularity or something analogous? There probably are.