For most purposes, mailing something to yourself for the postmark and keeping the envelope sealed would probably be adequate. It's possible to forge, but tricky enough.
You put postage on the letter, and the post office stamps the postage (to invalidate the postage). The stamp contains a date. You can't stamp something after having mailed it, that happens as part of the mail submission.
What confused me was how you would achieve post office stamping over a seal that's on the wrong side of the envelope, where the flap is.
Note that you need to send First Class to get a postmark in the US - not standard Priority Mail.