There is no exact timeline for sponsorship, but right now, it is showing as 9 months for inland, and 12 months for outland.
AoR, generally, can take at least a month to arrive, though this is not exact. Mine took several months to show up (submitted Oct '22. got AoR in Jan '23).
Every one's application is different, but in my wife and mine's case, we got my sponsor approval and her medical exam request on the same day, and her biometrics request letter about two months later. We had a very long wait after that, though, but we had some unusual circumstances with our application lol.