You have a right to enter Canada as soon as you satisfy the border officer that you have the permanent resident status, which nowadays can be easily verified against electronic records (assuming you acquired the PR status in the past 20 years).
However, to board an international flight to Canada as a national from a visa-exempt country (except a U.S. passport holder), you must either prove your PR status with a PR card or travel document, or have an electronic travel authorization (eTA). The eTA requirement is strict and the airlines can verify the eTA status with the Canadian authorities: without a valid eTA, the airlines will (are supposed to) receive a do-not-board message, unless you present a recognized PR document.
An eTA cannot be granted to permanent residents (unless you lie in the form, which may be considered as misrepresentation and can have serious consequences, although in practice it may be rare to prosecute). The special authorization available to certain Canadian citizens does not extend to permanent residents.
The situation is different (in practice, at least in recent times) for permanent residents from a visa-required country who have an apparently valid visa (though technically invalidated by their PR status), who may be allowed to board based on the temporary resident visa, though this (technically not allowed) workaround may become impossible due to additional advanced passenger information verifications.
You can, however, fly to the United States with a valid U.S. visa or ESTA (assuming you are eligible for the American visa waiver program) and exercise your right to enter Canada at a land border after you are admitted to the United States. That is the usual solution recommended for people who want to do it "correctly", though at additional costs.
In emergency/humanitarian situations, you can ask for expedited processing of your PR travel document with the webform or telephone the concerned consular section directly.
