Mindboggling complexity in abiogenesis? We don't even know exactly what mechanisms were involved, but they're more likely to have been a series of small, simple steps rather than one or two mind bogglingly complex cascades leading to fully formed life.
You're correct that many of the life forms we see today are, in fact, extraordinarily complex. But that complexity arose from small, explainable,
self perpetuating steps over aeons.
There are mutations with every round of reproduction. Those conferring useful traits tend to be passed on, they self perpetuate. As time passes these can accumulate and the organisms become more complex. No miraculous poofing of modern, complex physiology needed.
Complexity can arise from just a few, simple rules or algorithms. The Mandelbrot set comes to mind, or this well known little video of blind watchmaking: