Not discouraging further responses, but u/restricteddata has written about the atomic bombs and how they were created quite often. Here's the relevant section of the FAQ. Of particular interest to you may be u/restricteddata's AMA about the Manhattan Project.
Just to give some brief answers to your specific questions:
"How was the idea of a nuclear bomb first manifested?" After the discovery of radioactivity and the amount of energy locked up into atoms, the possibility of releasing all of that energy at once in an explosive fashion was considered by a lot of people, including scientists (e.g. Frederick Soddy), science fiction authors (H.G. Wells), and even statesmen (e.g. Churchill wrote about it), from the period of the early 20th century. It wasn't until the discovery of nuclear fission in 1939 that there was a concrete mechanism for how it would work, though. But the point is, there were people "primed" for this possibility prior to the science really being possible, and once it was, several people (Leo Szilard was first, but others followed) saw the possibility of making a weapon out of it.
"Did the Manhattan Project start with tiny nuclear bombs during testing and gradually make bigger bombs?" Not really, no. The idea was always to make a big one. Now, you can do some testing of a nuclear reaction on a smaller, non-explosive scale (e.g. criticality experiments, which are notoriously dangerous) but these are not really smaller bombs. Nuclear weapons are exponential systems, so one tries not to get them going because they quickly become very large. In some respects it is harder to make a "small" nuclear weapon than a "large" one (at least by the standards of the World War II weapons — which later became regarded as "small").
"Who was the first person to create a nuclear explosive of any size?" The first nuclear explosion was the Trinity test, created by lots of people (thousands of scientists, with hundreds of thousands of laborers to produce the nuclear fuel).