It's evident that Yui's been in love with Hachiman quite early on in the story. I always thought that it started right after her matter with Yumiko's been solved (I think it was episode 2 of the anime).
But the issue with her cookies for Hachiman in the last episode of season 2 made me doubt it. It's clear that they're meant romantically, and it's been hinted that the ones she gave him in the very first episode were also meant that way, which would mean that Yui loved him since the beginning of the story. Although, I'm not completely sure if I understood it correctly. The cookies in the first episode could have also been just her way to thank him for saving her dog.
Regarding Yukino, it's very difficult for me to find the moment she started to fall in love with Hachiman ("started" because I believe that she fell in love with him slowly over time) as she doesn't express her emotions as much as Yui, and for most of the first half of season 2 her relationship with him had been "overshadowed" with their confronting principles (maybe not a good description of what actually happened, but you get the gist of it).
I think Yukino started to love Hachiman shortly after their "dispute" was solved in episode 8 (s2). That is further supported by that picture of herself with Hachiman from the amusement park she'd kept behind her plushie on her bed (see episode 2, s3). Thanks to a Reddit post I've realized that the paper sheet Yukino quickly put away after that waterfall scene is most likely that picture.
Maybe another interesting fact: according to a different Reddit post, that plushie was the one Hachiman won for her. Unfortunately, I don't know if that's true as I can't remember having seen it in the anime. Maybe it was depicted in the novel?
But maybe she loved him even before they solved their dispute but there was simply no moment in which she could have expressed it (properly) because of that dispute. Or maybe a reason why Yukino became so upset with him after his fake-confession to Hina was that she cares greatly (and romantically?) for Hachiman and doesn't want him to get hurt any longer with his methods.
Going further back: at the end of episode 13 (s1), there's a scene that might hint that Yukino has already started to fall in love with him (she blushed when Yui pointed out that Yukino also watched Hachiman during the sports festival), although it could be also interpreted that she cared for him as a close friend.
Worth mentioning is also Yui's monologue after finding the picture behind that plushie on Yukino's bed. If I understood it correctly, she already felt being "the third wheel" for a long time. Maybe that hints that Yukino's already started to love him in season 1. Or it might be that Yui simply felt their "good chemistry".
A scene that might support the first one is the confession-scene in episode 11 (s3, 18:40+): Hachiman asks Yukino to allow him the privilege of distorting her life. Yukino then tells him that both of their life's already been distorted from the very beginning and Hachiman further says that it's only going to get even more distorted.
A Reddit post came to an interesting interpretation: it said that "distorting" here means to become so much involved in the other's life that it's being distorted. And the only relationship that could accomplish it is a romantic one. It concluded that Yukino actually said she and Hachiman had been in love "for the longest time" (so likely also since season 1). But does life really only become distorted when a romantic interest (or relationship) is involved and not already with e.g. simple friendship?
When did Yui and especially Yukino (start to) fall in love with Hachiman? If there's no clear answer to that question from the anime's perspective, does the Light Novel give an answer to that or at least obvious hints?
