First observation about the development of the Sisko-Kira dynamic is that there are several moments in the very early episodes where Sisko extends trust towards Kira despite the friction between them. In Past Prologue, she insists that she should accompany Tahna Los on the runabout for credibility when he goes to make the exchange. Sisko goes along with it despite his reservations, because he listens to her reasoning and realizes she’s right. And this is the same episode where earlier he was laying into her for going behind his back with Starfleet Command, and where he was suspicious as to the extent of her involvement with the Kohn-Ma. In Babel, right when Kira’s about to storm off to abduct Dr. Surmak (insane of her), Sisko tries to stop her, but relents when Odo points out that they’re in a pretty desperate situation.
And I think that pattern really lays the groundwork for her stated willingness to work collaboratively with him at the end of the season. In the pilot, when she’s hostile towards him, he says that he specifically requested a Bajoran First Officer. His later behaviour shows that it wasn’t just a symbolic request, and that he does value her input and shape his approach based on it.
(It’s also interesting that in both those examples, Odo is acting as something of an intermediary between them - the Babel example, and the fact that in Past Prologue, when Kira confides in him about her conflicted loyalties, he gives her a nudge towards telling Sisko everything by calling Sisko to his office, which paves the way for Sisko trusting her to be a part of the plan to apprehend Tahna.)