Mail gets sent out on Saturday by 4:00 PM to 4:30 PM depending on your post office.
The mail gets picked up at my post office at 4:30 PM so you must have the mail deposited into the mail box for outgoing mail before 4:30 PM for the mail to be picked up.
If you mail something after 4:25 PM or 4:30 PM then the mail won't go out until the following Monday since Sunday the post office is closed.
The USPS sorting facilities are still sorting mail after 4:30 PM and on Sundays as well but the mail is not picked up on Sunday.
So make sure to mail the letter or whatever it is you're mailing before 4:00 PM to ensure it goes out that day if you need the mail to go out that day.