1) Make sure you are getting the Canada Child Benefit.
2) If you received Employment Insurance maternity or parental benefits, these count
towards the $5,000 “work” earnings in the last year in the eligibility for the Canada Emergency Response Benefit.
You can’t get CERB at the same time as EI maternity or parental benefits.
If you don’t have work when you come off of maternity/parental benefits, you might get CERB if you have the $5,000 in work income in the last year.
In normal times, people who are coming off of EI maternity/parental benefits and have lost their job can apply for EI regular benefits (see here). Right now, CERB is replacing EI regular benefits and people who would qualify for EI regular benefits can still claim those, if they need to, if they use up all of 4 of their CERB payments.
If you get CERB for the same 4 weeks that your employer gets the Canada Emergency Wage Subsidy to pay you, you may be asked to pay back your CERB.