There is evidence the the prokaryotic cells did come before the eukaryotic cells but of course, it is not 100% certain. From previous inquiry questions, we have found that the general agreement as to when the Earth began was 4.8 billion years before the present in which the atmosphere consisted mainly of water vapour, methane, carbon dioxide, carbon monoxide, nitrogen and ammonia gas. The climate was also much different, but mainly stayed hot and humid. Electric stroms were frequent and so was volcanic activity, so you can imagine that the world was quite hectic but so full of energy. It was also mentioned in previous inquiry questions that Stanley Miller, a chemist back in the 1950's , supported the theory that life arose due to the right conditions at the right time, which happened to be 3.8 billion years before the present. 

 

It is believed that the earliest life forms were primitive photosynthetic prokaryotes known as stromatolites (we know this thanks to the fossils of their remains from billions of year ago). Further study has found that these stromatolites were also autotrophic and anaerobic, meaning that they could produce their own energy and oxygen without needing oxygen to thrive. Through growth in numbers and with more generations being produced, these stromatolites began to overule and were able to change the composition of the atmosphere- namely the increase in oxygen production. This increase in oxygen is thought to have been a deciding factor in the evolution from the prokaryote to the eukaryote as we know that eukaryotes respire only in the presence of oxygen. From these stromatolites, scientists have hypothesised that these prokaryotes inhabited Earth for almost 2 billion years before the eukaryotes developed. 

 

There is also another belief as to how the prokaryote became the complex eukaryote it is today. This 'theory' states that the evolution occured in 2 main process: 1) change in cellular structure and 2) endosymbiosis. 

 

Firstly, we know that the prokaryote at the time had a nucleotide floating aroun in cytoplasm within a plasma membrane. The first step was the infolding of the plasma membrane itself, which resulted in the creation of organelles such as the nucleus, golgi bodies etc. The next step was endosymbiosis. Endosymbiosis is the process describing a cell's 'digestion' of another living organism into tis own body for use. In this case, the newly formed prokaryote (technically a eukaryote now in definition as it has a nucleus) took in other prokaryotes such as mitochondria and lysosomes to function for its own personal use. This updated version of the prokaryote is the beginning or ancestor of the eukaryote cell today. 

 

We can support the theory that the eukaryotic cell did in fact occur due to the aforementioned steps by looking at the structure of the organelles itself. By looking at the mitochondria and chloroplasts, we can see that their inner membranes are similar to the plasma membrane of living prokaryotes today than in the eukaryote cells they are found in.  They also replicate by splitting, which is the same manner in which prokaryote cells divide. Finally,the eukaryotes have circular like DNA  (like prkaryotes and this information can be refered to in the 'What are the differences between Prokaryotic and Eukaryotic Cells?' section) and they have their own protein manufacturing system (including ribosomes) which means that they could have once been an independant prokaryote before endosymbiosis. 

 

All this information, knowledge and theories are fascinating but we don't actually know if they are 100% correct or not. The only way we would ever know was if we went back in time, but that would not be possible. At least, not yet...