I take it that this is a general question about how composing music works. You are not asking for a ready to go method for you to practice it yourself.
I wanted to post this as a comment, but the story is too long.
The question inevitably leads to a discussion or at least a very long list of considerations. I feel that you are mostly interested in an explanation that you personally can imagine. But some composers do seem to work with a strike of genius, something you say you are not interested in. Composers do or did exist who can manage all information at once. But other great composers were probably always struggling, working very hard to get to a satisfying result. Compare it to a painter. One may have a complete picture in his mind and know exactly what materials and colors to use right away. Someone else might just start with an empty canvas and put paint on it and see how it works out. Yes, a symphony can start as a piano piece which is then branched into different instruments. But it could just as well start with the composer thinking about certain instruments and using the piano piece as intermediate.
Then you say you are not interested in technical stuff like notation. Reflect this on your programming experience and see how it sounds. Notation and the accompanying language represent possible building blocks and rules in the creation process. But ok, in art, as far is i know, it is fully legal to ignore them.
So there are many answers to your question, it is up to you which ones you like the most, but in general very different approaches of composing will turn out to be equally valid. Better still: all methods are allowed at the same time, that's the fun of it!