Until you have either lived together for one full year, or get married...you can't even start the sponsorship process.
The fact that you do not qualify [yet] and the fact that he's already out of status, really makes it difficult for the both of you. Yes, he can technically apply for sponsorship without legal status, but it will be a lonnnng process (over 2 years if submitting an Inland application) and he would not be eligible for a work permit for ~ 17 months after the application was received by CIC. It would be another couple of months after that before he actually received the Open Work Permit. There is also NO guarantee that he would be allowed to remain in Canada during the process. Most are, but not all.
Another option would be for him to leave Canada, as soon as you have met the requirement to sponsor, and submit an Outland application.