How can the melting temperature of PCR primers be so far below the extension temperature?
Note that 'melting temperature' is actually about POPULATIONS--it's generally the temperature at which 1/2 of all of the millions of copies of 2 things will be stuck together and 1/2 apart. Once stuck, not all primers will leap off the template simultaneously even at much higher temperature... As you indicate, there's nothing to stop the polymerase from starting its work (extending the primer) before the extension temperature.

And, as in another answer, polymerase can add stability to the pairing.