You can't meet someone then conceive him afterward time linearness or not.
Why not? Sounds like a needless and arbitrary limitation - time travel is all about looping and iterating and having effect precede cause, no matter how you look at it. It shouldn't be much of a trick for the Prophets to meet Sisko, and then decide that this is such a cool guy that on the next iteration he shall be divinely conceived.
Also, "not experiencing time linearly" doesn't mean "not experiencing time at all" let alone "experiencing everything at the same time". It just means time is experienced in some different, unspecified manner. Humans don't experience it "linearly", either: the subjective experience is at best "monotonic" in mathematical terms, but looks more like a roller-coaster ride than a neat line, what with time flying when you are having fun etc.
Asking why a human became "the" Emissary probably misses the point. Sisko was "an" Emissary; in other realities, there were competing individuals such as Akorem Laan, and at other timepoints of Sisko's own "timeline", there may have been further Emissaries, too. Things just happened to work out favorably when Sisko was holding the title, and the camera happened to be present, so we're a bit biased here.