To change your payment method, you must be a billing administrator.
To see the current administrators, go to the Google Cloud Platform Console, open the left side menu and select Billing. If you have more than one billing account, select the billing account name. You'll either see the current list under Request access, if you aren't an administrator, or in the Permissions panel on the right side (if you don't see the Permissions panel, click SHOW INFO PANEL).