That’s usually the case for a Non B as most companies can’t (or won’t) supply the vast amount of paperwork to apply in country. Teaching positions are slightly different and it may be possible for your new employer to let you apply in country (rare but can happen).
You need a job (offer) in order to apply for a work visa then work permit. Enter on a tourist or exempt entry. Find an employer and then go from there.
Part of the application process would be to show your present location (entry stamp to that country and hotel booking etc). If you don’t have those then they’d probably deny the application.
You can try doing it all within Thailand but my guess is that unless you follow their rules it may not work out well for you.
Then you probably don’t need a visa to enter again, but as it’s up to the individual officer you hand your passport to it’s impossible to say if you’ll have any issues.