It is certainly not impossible. The gestation period for a cat is normally between 6 and 7 weeks depending on the breed.
It would not be the first time that the routine procedure of spaying has been passed on to an inexperienced person working at the vet clinic and failed to check for pregnancy.
At 3 weeks the embryos are still very small and easy to miss.
A free visit to the vets who performed the procedure is a fair expectation, there may be other complications caused by the spaying.