Is a lot of puss normal after a tooth extraction?

Be cautious...: No, unless the tooth was extracted in an emergency situation where there was a large area of abscess or infection. The pus could just be draining normally. Consult with the treating dentist if things don't improve quickly.

If abscessed tooth: Then the removal could promote drainage, and some could/would be normal and beneficial. If the drainage is persistent and new after a few days, then you need further evaluation for non-resolving abscess, another source, retained root tip, another fascial space involved with infection that was not drained, infection tracked via needle, bony fragments, etc.