Timelines depend on which document you actually need and where your country prints its passports. Emergency travel documents, the limited papers that get you home, are typically issued within one to a few working days once your identity is verified, and that is the realistic fast path for anyone with imminent travel. Full replacement passports issued abroad are slower, because many countries print passports centrally in the home country and courier them out, so waits of several weeks are normal, and busy seasons or complicated identity verification stretch that further.
Identity confirmation is the variable you control. Applicants who can produce a copy of the lost passport, another government ID, and a prompt police report sail through; those with nothing may face interviews, checks against home records, or waiting for documents from family, all of which add days or weeks.
So the practical playbook: decide early whether you need the fast emergency document or can wait for the full passport, book the embassy appointment the same day you file the police report, and bring every scrap of identity you have. And going forward, cloud copies of your passport, a physical photocopy in a separate bag, and two spare photos convert this whole event from crisis to errand. Your embassy's website states its current processing expectations, which beat any general estimate.