no you can start anytime you want.

nope

Q. I have a pending adjustment of status application based on an approved employment-based immigrant visa petition with an associated job offer. Must I work for the petitioning employer while my adjustment of status application is pending? Am I required to be working in the same occupational field as the job offer while my application is pending? Would a period of unemployment while my application is pending affect my eligibility for adjustment of status? A. Noncitizens with pending adjustment of status applications are not required to work, or ever have worked, for their petitioning employer. An employer who petitions for a noncitizen worker is doing so prospectively. In other words, by filing the I-140 petition, the prospective employer declares their desire and intent to employ the noncitizen upon the noncitizen becoming an LPR. The noncitizen who is the beneficiary of the petition is not required to work for the petitioning employer before the petition is filed, while the petition is pending, or while the adjustment of status application is pending. However, when applying for adjustment of status, the applicant must demonstrate that the employer still intends to offer them the job and that they intend to accept the job when they become an LPR. The noncitizen is not required to be employed in the occupational classification of the prospective job while their adjustment of status application is pending in order to be eligible for adjustment of status based on the petition. Finally, a noncitizen with a pending adjustment of status application based on a prospective job offer may be unemployed while their adjustment of status application is pending and, depending on the facts involved, may remain eligible for adjustment of status. However, a period of employment in an occupational classification different from the prospective job or a period of unemployment may affect a noncitizen’s current immigration status and could raise doubts about the continued validity of the job offer and/or the noncitizen’s intention to accept the offered position after adjustment. (Added 9/15/2023)

it from USCIS websitw

@Barb B Thanks!

agencies want you to go and start working ASAP but don’t try to fall under their words. Try to finish your semester or even your degree before starting to work. This sponsorship means you will start after having the greencard, not after ead. Barb B have already posted the answer from USCIS and they clearly say there is no compulsion to work before green card. Even if they call you for interview, you can clearly say you will go and start working soon or after green card. I have friends who had their GC approved through interview before starting the work.

in my case, agency didn’t push me even though i wanna work for my sponsor asap to make living.