You can get isolated pockets of low entropy that appear (e.g. the human brain), but I think I've heard it described that there has to be thermodynamic pathways leading to such states. We understand parts of these pathways, but there are important aspects still left to figure out.
And of course, as you mentioned, the system as a whole is still increasing in entropy the entire time.
Imagine a mountain where height inversely correlates with entropy. The summit represents the very low entropy state of the big bang, and the second law of thermodynamics is an enormous steam-roller that is currently in the process of flattening the entire mountain. Then, us humans are simply pebbles that have been shaken loose and are dancing in the foothills. In a few billion or trillion or quadrillion years, all the dancing pebbles will have been crushed into a fine dust and spread across a perfectly flat, unchanging plane.
But they will have danced beautifully in the many years before.
This always confuses me a bit, why do we consider the first instants of the universe maximally ordered? A near homogeneous sea of per-subatomic particles seems less ordered than the later universe of galaxies and stars and hydrogen atoms with cold areas in between.
One point that seems not to feature in these debates is that this is all (physics) fundamentally subject to the constraints of language (maths) and cognition (human), we choose to describe things in a way that appears useful to us, but these judgements and perceptions are filtered by how we understand things. We are squashy and small and it is quite silly to imagine we really are thinking about these processes in an objectively meaningful way.
Note what happens as the universe proceeds from that time period to its heat death; hydrogen is burned into higher elements until everything is cold iron floating in space. In this case, it might be best just to look at the available energy as a proxy for entropy; a universe full of hydrogen is a low-entropy universe that still has a lot of useful energy that can be extracted, whereas in the heat death of the universe, there's nothing left. No fusion can be done. No fission can be done. No chemical energy floating around that you can use. Just balls of iron in maximally thermalized environments, all maxed out in entropy.
As I've occasionally said in other contexts, right now the universe is young and awash in energy in many forms; our energy problem is a difficulty in figuring out the right way to metaphorically cup our hands and capture it all in the ways we want to use it. We're literally billions of years away from an actual lack of energy, because the universe started out with a lot of it.
Much higher ordering is straightforward and is essentially just statmech:
1. Run the expansion history of the universe backwards: there are fewer degrees of freedom as the universe collapses into the big bang.
2. Run the expansion history of the universe forwards: vacuum is very high entropy (you can swap a bit of vacuum from here with a bit of vacuum from there and not tell the difference), and there is much more of it at late epochs. Assuming no-hair, black holes are also very high entropy, and there are more of them at later epochs.
Maximal ordering makes some assumptions about quantum gravity with respect to (1):
> A near homogeneous sea of per-subatomic particles
... would expand in such a way that the universe would remain (nearly) perfectly smooth at all epochs.
We can start with the idea that there is an inherent uncertainty to the energy of empty-of-particles space. At later epochs, this uncertainty is small; but in the very early universe it is large. With slow expansion, the uncertainties average out over short distances. However, during cosmic inflation, the uncertainties are stretched and only average out on much larger length scales. The "new" vacuum produced as inflation continues has prorgressively less energy uncertainty, but are "within" the streched uncertainties from earlier. By the time inflation ends, random regions of all sizes contain subregions of overdense and underdense vacuum energy.
Cosmic inflation precedes the hot big bang: it is the chaotic arrangement of vacuum energy at different densities that decays into matter (in the most general sense of matter) proportional to the vacuum energy density. More matter arises in the overdense regions than in the underdense regions. As expansion progresses, gravitation takes over: light finds it easier to leave underdense regions than overdense regions, and that (the gravitational redshift, and the spectrum being highly similar to blackbody radiation) means underdense regions look slightly hotter than average regions, and overdense regions look slightly colder. Gravitation also works on the rest of matter too, not just light: matter flows from underdense regions to denser regions; matter flows to overdense regions from sparser regions. Finally, overly-overdense regions will heat up and emit light and kick hot particles out. The balances between the vacuum energy fluctuations before the hot big bang and the gravitation-vs-radiation flow of matter afterwards are encoded in the cosmic microwave background.
> less ordered than the universe of galaxies and stars and hydrogen atoms with cold areas in between
The mostly-empty areas in between have much higher entropy, and those areas are even bigger (and emptier) at later times. The galaxies and stars and hydrogen atoms are not more numerous at later times: matter dilutes away with expansion.
Imagine the soil 50 years before Shakespeare forming the food he ate and the trees which became the paper he wrote on. It seems a lot like ash (soil) did organize itself to a lower entropy collection (with a lot of help from an external energy pool).
Also, many seeds didn't make it, so there is a bit of survivor bias looking at the one seed that did become a tree.