Apple itself has given the date. In a press release on its Newsroom site in China, the company said the first iOS 27.3 developer beta will arrive on Wednesday, November 4. Because of the time difference, that most likely means Tuesday, November 3 in the US.
Apple also said iOS 27.3 will reach the public in December, without naming a day. Past patterns point to the middle of the month: the comparable updates in recent years landed around December 11 or 12, just before Apple’s holiday break.
If you searched for iOS 27.3 beta 4, it isn’t out yet. As of early November, even the first beta has not been released, so a fourth beta would come weeks later, toward the end of the testing cycle. Apple has not published a beta schedule.