USPS is open and does deliver mail and packages on Saturday.
So if the mail you have coming to you that is First Class Mail and it arrives at your local post office on Saturday then the first class mail will be delivered to your address or your mailbox.
All mail runs on Saturdays and will be delivered if it reaches your local post office that is responsible for delivery to you.
If the USPS First Class Mail doesn't arrive on that Saturday then it will be delivered by Monday.