Is it possible for everyday people join the middle class via labor? What does the middle class mean to you?

I am a licensed engineer, 35, with a decade of experience. The best job offer I got was 127k in the suburbs of NYC. Couldn’t take the job pay was too low for area.

At least in high cost of living areas I think middle class is minimum 150k more realistically I think it’s 200k. What is the pipeline to make 150k?