That's the point, if you can't trust the connection, stop trying to come up with more complicated ways to use the untrustable connection and accept that there is no safe way to update time.
But since the vast majority of them do not fail in that matter if the normal, configured methods of determining time aren't working, using TLS parameters that have been deliberately randomized by standard for like what, a decade now?, can not possibly be a more straightforward failure mode than logging errors and waiting for operator input.
If it's that critically important, embed a fixed signature for a set of known time sources and query those as a last resort. Microsoft certainly has the resources to set up a few to do this the much more obvious and predictable way.