Thank you.
The link you posted states "Note: Birth certificates, Social Insurance Number (SIN) cards, bank cards, credit cards, and previous Canadian citizenship certificates are not accepted as personal identification for this application process", but the checklist says a birth certificate is sufficient. Hope it's correct!
The link is giving instructions for both minors and adults. Notice the language about minors who do not have photo ID.
Then look at the list of acceptable ID and the ones in the "Note:" - the difference is the ones they are not accepting for proof of identity are lack of a photograph.
Side note: if you'll want to apply for the child's passport before you get the citizenship certificate, keep a complete copy of the application for citizenship cert (and all docs submitted).
Basically the procedure is you'll apply for a passport on basis that the child is presumed to be a citizen. Contact local consular section of canadian embassy or consulate and work that out.
It sounds weird but this is common because takes so long to get the citizenship docs.