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Yes they do.

See here:

https://accounts.google.com/.well-known/openid-configuration

And as far as I know, Facebook doesn't support OpenID Connect. They still roll their own custom OAuth2 implementation.

That is, obviously, not on gmail.com. I cannot put in my email address into a generic widget and have that come up - the URL has to be hard-coded into the RP, and the RP additionally has to be configured with client authentication details. This document cannot be autodiscovered from a user identifier as per the spec, and provides absolutely nothing over hard-coding the configuration it contains.

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