Can a Teacher on Visa Waiver Apply for a NON-B Visa Without Leaving Thailand?

if your local Immigration Office can not make this conversion, then you have to go abroad to visit a Thai Consulate and apply there for a Non Immigrant B visa. Check their website for the documents needed or ask your school to contact them to be sure.

It is... IN THEORY. It depends on your immigration office and your school though.

First you visit with an employee from the school the MInistry of Labor and ask the hand out with the requirements for the Work Permit. Then you visit your local Immigration Office and ask if it is possible to convert your entry stamp into the Non Immigrant B Visa, if yes than you ask the hand out with requirements. Go back to the school get all requirements done apply for the Work Permit and than for the Non Immigrant B visa. Relax until you have the visa stamped inside your passport and the Work Permit in your pocket then you start working.

It can take a while for the school to get the documents together. Im not sure if you can do without leaving Thailand. I may be wrong.

Yes you can with the correct paperwork

If you have enough days left on your current stamp visa exempt entry, not visa waiver

AND

if your employer can prepare necessary documents in time

AND

if your local immigration let you do inside country application,

Then it is possible

Ask immigration