How did the very first cell come into being?

Miller's experiments produced 20 amino acids and other organic compounds including: ATP, lipids, some sugars, and the bases of RNA and DNA. The main problem of organic synthesis is how did these molecules develop without the aid of enzymes to speed up the reactions? Sidney Fox, of the University of Miami, dripped a dilute solution of organic monomers onto hot sand, clay , and rock. The water vaporized and left behind polypeptides he called proteinoids. Clay was abundant in prebiotic earth. Clay has the ability to act as a substrate for this type of chemical reaction. The charged sites on the clay attracted monomers in such concentrations to bring them into close proximity for chemical binding. Once these organic compounds were produced, aggregates of these proteinoids self-assembled into small spheres called protobionts. These small spheres were capable of osmotic swelling and shrinking and even able to produce a membrane potential.

It seems you haven't looked very hard. There are quite a few possible explanations. A biology textbook should be a good start.