According to reporting by the Washington Post, Americans with the lowest income will get mailed checks first, Here’s the timetable for the first checks, per IRS documents seen by the Post:
The rest of the checks will be issued by gradually increasing income increments each week. Households earning $198,000 who file jointly will get their reduced checks on Sept. 4. The last group of checks will be sent on Sept. 11 to those who didn’t have tax information on file and had to apply for checks, according to the Washington Post.
If you're eligible, you should receive a stimulus check.
Please see TurboTax's Everything to help you get your stimulus check as soon as possible page to see if you qualify for a 2020 stimulus check, and how much you might expect.
See KatrinaB48’s timetable above for mailed stimulus checks; since you’re posting your question under a mailed check question, that should answer your question.
If your check would be Direct Deposited, there’s no timetable for that, but it would most likely be much quicker.