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Improvising, screwing around, experimentation are great ways to generate ideas. I think most composers work this way, most generally don't start with some huge structure, they just find some germ cell ideas by improvising that then can be build upon afterwards with analytic techniques. I think there are two main approaches, the intuitive feelings and pure ear based approach which is what most people call the "talent" aspect and the analytic approach which is a lot like mathematics, it is about studying structure, and is a learned skill. The best composers will use both of these together. You should learn chord structures, scales and how to read sheet music. This will allow you to conceptualize a musical idea as a concrete mathematical object, and it will help you to not lose the idea. The reason you forget the music in your head is because you don't have enough reference points to define it in a memorable way.

You can understand a musical idea as a kind of memory impression, an echo that you can play back in your head, and also as a pattern of pitches and rhythmic structures . Having two reference points , sensory and abstract mathematical is very useful.

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