Oof this is a toughie.
I think Mulder fell first, or was at least aware of it first. I genuinely don't think that Scully became aware of her feelings until season 6. Mulder, I think realised in season 5.
So Mulder I think realised around Redux II that his feelings were deeper than friendship, I don't think that he dealt with that realisation though until Fight the Future when he almost kissed his best friend. From then on, in my opinion, he broached the subject again (poorly in Triangle) and then not receiving a warm response, decided not to attempt to act on them again. I think he's slightly hurt, but he respects her and doesn't want to push it.
Scully, she's tougher to understand. Hyper-rational and a consummate professional, I think that she realised during The End that she had feelings for her partner beyond friendship, I don't think that she fully understands what those feelings are until season 6, and certainly not until after One Son. In my opinion, this led to a slightly disjointed relationship in season 6, if they both realised that they were in love earlier, surely Arcadia would have had a completely different vibe. Mulder's reticent and neither seem comfortable with the physical aspect of the assignment.
Once we get to Milagro, Padgett's concession that 'Agent Scully is already in love' seems to have been the catalyst for a change in their relationship. Mulder starts paying attention again. Immediately following Milagro we have the Unnatural and the batting scene, in my opinion, this was Mulder with a regained sense of hope.
Sadly, Biogenesis and Amor Fati didn't give enough away about what Mulder may or may not have heard in Scully when she visited him in the hospital, but I'd like to think that he was able to understand how she felt about him a bit more clearly in those episodes. Perhaps even came to understand her reasons for not moving their relationship forward. Season 7 is flirty and fun, we get our first kiss, rubbish as it was, but I don't think that they ever discuss their feelings during the season. I'm not sure where the baby request fits in to this season either.
I don't think that Mulder even contemplates seriously a relationship with Scully until after Closure, when he's suddenly 'free'. I don't think that she contemplates a relationship with him until after All Things. I don't think they consummated anything in that episode either. I don't think anything happened until after En Ami. By Je Souhaite, we seem to have some RST.
I don't know... it's just so tough.