Thank you for your reply.
Canadian embassies overseas is a joke! I am sure there is at least backlog of 6 months. We might consider though that temp passport, if needed.
I have many contacts and friends who have got the temp passport for children. Timeframes I have heard are less than two months - but ALL of the people I have spoken to about this have said getting their own documentation in order (birth certificate etc) has been the limiting factor. (Most have said their own organisation of travel with an infant was the biggest delay).
None have said that the embassy in the end was the problem (eg if they had a real emergency they'd have been able to get sooner).
However - all have complained the hardest step was getting a response from embassy - terrible these days (hard to get a human on the phone, hard to get a written response that is non-form letter).
All I can say is - for this one needs the CONSULAR section, not the visa section. And the global consular help line is worth trying.
I've not had this particular experience myself though so can only report secondhand. YMMV.
Important to note - the embassies cannot deal with or help with the citizenship certificate. Not their fault. That's Ircc in Canada. The embassies can issue passports (temporary, emergecny, etc) for those they know or believe to be Canadian citizens.
For infants whose parents can show they are citizens (not by descent), that's what they do - issue documents based on presumed citizenship status. This is actually quite common and not a big deal (proof of birth in Canada or naturalization usually enough). I believe a Canadian passport that shows a place in Canada as place of birth is usually enough.