No, Man A is not the father.
The gestational-age count of the length of pregnancy doesn't begin at conception, it begins on the first day of your last period (or on a calculated first day of your last period if the embryo's measurements seen in an ultrasound don't match your actual last period). In either case, the GA count of weeks "pregnant" does not start on the day of conception, it begins two weeks prior to that. So if they did an ultrasound and told you that the embryo is measuring at 6 weeks, they meant you were 4 weeks since conception.
Did you have an ultrasound, or was this measured by the doctor pulling out a little cardboard wheel looking at dates?