unfortunately, you will need to adjust your expectations.
It is presently taking 2-3 months to receive the Acknowledgment of Receipt for a complete application. If your application is missing something, it will likely be returned to you a little sooner, but there is no fixed amount of time.
Not sure what you mean by "will the waiting days for AOR be taken into totally processing time?" Your "processing time" is from the date that CIC receives your application, so your processing time includes the time before you receive your AOR. However, that means nothing in terms of when you might expect the application process to be completed. Some are finalized within 6 months, some within 2 years. Every application is different, and processing timelines change as CIC changes.