Hi! Do not take my word for it, but I think some people managed to get accepted without having their 4 references, but it might depends on more factors than what I am entitled to know, and from what I can see, things have changed in the last few years. A recruiter even told me something that contradicts what was written on the form: The recruiter told me I could put past employers (e.g. a superior from a past job that I had between 2002 and 2003) and more recent ones to even things out, while the form specified that overall, the 4 references had to cover the last five years entirely. After the CFAT, they told me that the form was correct, and that it had to cover the last five years, meaning that if I had no contact with them in the last five years they wouldn't be considered as valid references.
To a lower extent, my situation is similar to yours: As I have been out of school for almost three years and since I am self-employed or employed within my parent's business, there is a two years gap (and still growing since I applied) where I had no professional contact with any valid superior. If anything, there were other employees, but they were either my equal or my subordinates, meaning they couldn't be considered, and I have no family doctor (as it's near impossible to have one in Quebec unless you're older, really sick or have children).
They told me that obviously, I wasn't the first self-employed applicant and that while it could make the background check take longer to process, it was not an automatic rejection. If anything, I will have to explain everything in a subsequent interview.
Try to find someone who have known you for a least a year: it might be a mentor, a personal trainer, a member of a religious order that knows you well enough and the like. Be upfront and ask a recruiter.