USPS does deliver mail on Saturday.
Saturday is a business day for USPS so since they deliver mail to the post office the USPS will also deliver mail to your curbside mailbox or house.
The actual time for Saturday USPS mail delivery varies but for my house I get my curbside mail through USPS on Saturday by 10:00 AM and on Monday through Friday my mail usually gets to me by 8:00 AM to 9:00 AM.
The USPS sorting facilities are open everyday of the week 24 hours per day sorting mail and sending it on it's way.
But the local post offices are closed on Sunday and Federal Holidays but the mail is still being sorted and transported.
You should get your mail on Saturday if you're expecting mail.
But the mail must get on the postal deliveries truck before they leave out which is usually around 7:00 AM or before.