Hi
For your boyfriend to sponsor you, you must either get married or live together for a year to become common-law.
There is no fast track. You would need to look at Quebec's specific requirements to see if you qualify. As far as I know (this is not an immigration program that I have looked into very much), you must have a job offer, already be working or have studied in Quebec to qualify. If you do qualify, you need to apply to Quebec for a CSQ. After receiving the CSQ, you would then need to apply to IRCC for PR.
You haven't stated your nationality. Depending on where you are from, you can look into the IEC program. Otherwise, if you want to work before becoming a PR, you would need a job offer from an employer with a positive LMIA. It is difficult to find such an employer, as the process has very specific requirements, costs $1000 and takes several months.