Chưa means "not yet". If you put it on the end you make similar structure like the one with không.
người đàn ông chưa bắt đầu. (the man has not started yet.)
người đàn ông (có) bắt đầu chưa? (has the man started yet?)
"the man does not start yet" corrected me for "the man did not start yet". And we gots "the man has not started yet." above . And as an extra added attraction it is suggested "the man has not yet started". by gentle readers. I'm laying my bets on "The man does not start yet" to avoid the past tense issues.
This one is super annoying what the hell is wrong with the man has not yet started