Let's look at why Sisko was born first. A Prophet took over his mother Sarah's body and stayed in/with her long enough for her to meet and marry Joseph Sisko and for them to have a son. Then she bolted.
If you buy that story as legit, then it's not too farfetched to assume that a Prophet came back, took over some admiral at Starfleet Headquarters human resources office and put Sisko on the short-list for commanding Deep Space Nine.
Alternatively: Aren't we told in "Homefront" or "Paradise Lost" that Leyton was the one to recommend him for the DS9 posting? is it possible Leyton was already power-hungry and planning his big bad coup beforehand and wanted Sisko at DS9 "out of the way" (in case Sisko sided against him) or in command of DS9 at the nerve center of Bajoran/Cardassian political turmoil at a time when tensions were escalating with the Cardassians?