With OET all the eukaryotic features, such as organelles and sex, were created successively from the start of life in the simplest form. This simplest form was not a bacterium, as the endosymbiosis hypothesis holds. Neither archaebacteria, nor eubacteria existed at the time. The first cells originated in the RNA world, and they were quite similar to the nucleus of modern cells. In the RNA world, catalysis was controlled by ribozymes, not enzymes built from proteins. Genetics were primary also built on RNA, but DNA came into use for long term storage, much as we see it today. With the invention of translation, which was, and also today mostly is, built on RNA structures, separation into two compartments was a benefit. Special channels in the outer membrane were created. Bubbles were "blown" from these, and eventually all the bubbles united into the cytosol. With this separation the control system was well protected, and it was possible to use simple single membranous organelles. They were used to import and export metabolites from the environment. Later, also double membrane organelles were created. Viruses were created as a way to transport genetic material to other organisms, and commuting organelles were created to transport whole systems between organisms. As these could be autonomous, they could however also be used by just commuting to the environments. They became the bacteria, as described elsewhere.
With the endosymbiosis hypothesis the simplest eukaryote cell was not the nucleus, but a bacterium. Very often an archeabacterium is used as the source for the eukaryote in the various forms of endosymbiosis theories. The various forms of the hypothesis, described respectively by Lynn Margulis, Tom Cavalier-Smith and Martin & Müller propose different states of evolution of the host that received the bacterium that became the mitochondrion. But common to all of them is that evolution had a boost following this event. Features like sex and a series of organelles were invented after this event, mainly in the toxic world. In OET all these basic concepts were invented in the anoxic world, long before any bacteria existed.
The separation of the eukaryote into a nucleus and the cytosol has not been given any good explanation in the endosymbiosis hypotheses. Margulis saw the nucleus as just another organelle, and assumed that it was also the result of some endosymbiosis event. Martin & Müller may have a better explanation, but they are all quite speculative.