Over-analysis engaged...
2237 - Claire buying a coffee for Marten on the second day. Her explanation seems genuine considering her seriousness about being a librarian. Claire's angry (rather than embarrassed) reaction seems to back it up. I don't think it's an indication of a crush.
2272-2281 - Bonding Through Coffee Shop Walks
2272 - Panel 4 "What about me?" - for joke purposes only?
2322 &
2323 - "You say you're my friend. Will you still be my friend if I tell you my secret?" Claire doesn't really have any close friends that we see in the strip, so not sure how she usually deals with other people on this issue. Claire takes a risk by telling Marten, looks a bit surprised by Marten's response (she was probably expecting different) and then her happy expression (I'm not really sure what to call that expression) in panel 5. I don't think there's a crush yet, but trust is there now.
2327 - Claire is happy that she told Marten, panel 1
2362-2367 - Bonding Through More Coffee Shop Walks
2370 - For me this is the first overt indication of a crush or at least a high regard for Marten. Though Claire's 'luckyyyy' is a bit ambiguous as to who she thinks is lucky, because Dora is emphasised I think she means Dora is lucky.
2372 - +1 Bonding
2377 - Claire's offer to give Marten a lift to the wedding.
The Wedding Arc - What might've been a background crush is brought to the forefront. Marten and Claire basically are together for the whole weekend right? There's a few strips to choose from in this arc, here are two:
2390 - The tie tying where both are blushing
2403 - Flirting panel 6?
2431 - Flirting detected panel 3
2435 - Ding ding ding. Icing on cake in panel 3. Claire sees that Marten isn't put off by the episode. So Claire starts seeking out Marten outside work hours in
2445. At which point it is crush confirmed.
In summary, Her crush is arguably there during the wedding arc and I would say definitely present immediately after the wedding arc. It's difficult to pinpoint when it started.
I submit that her crush developed between the lake party and strip 2370 - I think they probably made additional off screen coffee shop trips where it developed.
/over-analysis