Neither the universe, nor the earth, nor any appreciable part of the natural world, is a "random system". They are systems of law: the laws of nature. Furthermore, since the laws of nature are a single system, and ultimately connect everything -- connect all systems -- spontaneously arising order in one system, or one part of a system, can, and often does, generate order, and/or increase complexity, in other parts of the system.
Once you look around a bit it's a fairly obvious characteristic of such a system, of this world, that "spontaneous appearances of order" often start simple and then, because of these connections, get more complex, even before getting to biology.
For example convection cells spontaneously appear in a system where heat is unevenly distributed, not because anyone makes or designs them, but simply as a result of the laws of physics. Consider all that comes from that in the case of our own earth:
Assume that this planet did indeed begin as a simple molten mass. A big, hot ball will cool. But the laws of physics don't allow it to cool evenly. Heat escapes from the outside, so the outside cools more quickly while the inside remains hotter. In consequence convection cells form in the earth's interior. Because the molten material in the earth contains lots of iron, that orderly movement creates a magnetic field. That magnetic field creates a barrier around the earth which deflects the most energetic and destructive particles from the sun. This allows the earth to develop and maintain a complex atmosphere. That allows complex and orderly systems like weather to develop.
The magnetic shield also allows chemical compounds to exist on the earth's surface which would otherwise be destroyed by the energy from the solar wind. It creates complex (and beautiful) phenomena like the Northern Lights.
The convection currents in the earth's interior also move the earth's crust, driving continental drift, in consequence causing mountains and continents to rise.
All this, and much more, from the simple cooling of a big, hot ball.
OK, so the laws that operate the system allow for the second law to be temporarily overridden.
Where did those laws come from?
Weather is not that orderly. There is much disorder in the systems, which is what makes weather forecasting so much of a crap shoot.
The slight amount of order that appears for some time in the formation of low pressure cells, hurricanes, and thunderstorms, dissipates very quickly.
It isn't merely the unequal heating of the earth's surface that causes the weather systems to develop either. There are other forces that play into it.
Still, even the slight, transient amounts of order that appear in weather systems, are magnitudes of order removed from the order contained in DNA, and the information it carries.
Extrapolating the complexity of life from something as unstable as weather is not reasonable.
While weather is a good example of how just poring energy into a system can produce slight areas of order, life isn't. To achieve that degree of order and information would require massive amounts of disorder to exist elsewhere for the system to balance out and looking at the universe as a whole, I just don't see that kind of disorder in evidence.