For one thing, I'm looking at the uniforms, and it wasn't until Rapture that DS9 got the new ones. It seems to make sense that Rapture is the first episode to take place after First Contact. And, considering what Memory Alpha has to say about the "behind the scenes" info concerning the uniforms, it's the closest thing to a continuity hook we've got if we want to place it accurately. It says:
"This was the first episode of Deep Space Nine to feature the grey-on-black Starfleet uniforms created for Star Trek: First Contact. Sisko also wears a captain's vest/waistcoat, as worn by Jean-Luc Picard in that movie. The uniforms had been held back in production so that they would not be seen until an episode that aired after the official release of the movie. Noticeably, Avery Brooks' tunic does not appear to fit him correctly, making correct positioning of his combadge difficult. For the duration of this episode and part of the following one (DS9: "The Darkness and the Light") he wears the combadge on the grey portion of the tunic instead of the black; the combadge was positioned correctly in all subsequent episodes. Furthermore, Sisko does not have the red stripe around his cuffs that all the other uniforms do. Bashir's "Does my uniform look brighter?" line was a not-so-subtle way of drawing the audience's attention to the new costumes. Besides all the admirals' (and Whatley's aide's) uniform which had not been changed yet, some officers of the lower ranking staff are still wearing the previous costumes. "
Actually, Rapture was the second episode to air after FC was released.
FC was released on November 22, 1996. Three days later (November 25 1996), The Ascent aired. Rapture was aired almost a month later, on December 30, 1996.