Hello Walter,
It's a good question. In the PMI's recent publication Process Groups: A Practice Guide, the Assumption log first makes an appearance as a Project Document (an output) in the Develop Project Charter process (Figures 4-1 and 4-2). Any earlier would probably not be a good use of time and energy, although I'd posit that assumptions are being generated from the moment an idea for a project has appeared in someone's mind, so the seeds of the log are already there!