Do I need to leave Thailand before my new company applies for my work permit?

Hi everyone. Thank you for all the advice you give everyday. Im Italian.

So the 1st of may i stop my non-b extension and work permit and i got tourist extemp for 1 month waiting the new company in bkk prepare all the papers for me. Now we we are getting confusing because talking to the labour office, they said that i have to leave Thailand before my new company apply for the work permit and it will takes around 3 days to get the letter. When i get the letter for the work permit i have to go to the thai embassy and i get the non b visa. It is right that i have to be outside Thailand before my company apply for the work permit? Thai embassy in Singapore is a good choice? Thank you in advance. I hope i give all the necessary information