Marriage alone does not give you the right to work in the U.S, you need to apply for a work permit.

If you're applying for a green card (adjustment of status) based on marriage, you can file Form I-765 for a work permit at the same time.

You cannot start working until your work permit is approved even if your marriage is real and your green card application is pending.

It’s smart to file the I-765 together with Form I-485 so you can work while waiting for your green card.