in my opinion, the INFP gave a pretty clear message: she is in no rush to meet you halfway. who knows what her reasons are but text replies like "haha" and "yeah" are standard fare lukewarm responses.
all you can do is decide how far you're wiling to take this. i see that you put your cards on the table (earlier than many INTJs i've known) and she didn't exactly respond enthusiastically. do you want to pursue someone who doesn't have the communication skills or certitude to respond to a red-blooded man's clear expression of interest?
This is true to a point. I imagine she would've expressed more disappointment at canceling & hope to reschedule or do something in the future if she was really interested. The response does seem quite lukewarm & like she's not too eager to make sure you do eventually go on a date.
I really hope she is not passively trying to turn you down... If you keep getting this kind of vague avoidance, then I'm pretty sure that's disinterest though.
How old are you guys again? If the INFP is younger than mid 20s, than not being savvy in romance & sending unclear signals is not strange. INFPs can be overly modest & need to be hit over the head that someone is interested in them romantically. Sometimes they don't know how to respond when they realize someone actually is interested. It seems easier to "run" from it than deal with the reality of it; part of that is out of a fear of being "exposed". Other times it's an oversensitivity to others' feelings; how do you let them down easy? So there can be a genuine obliviousness to a young INFP & an unfortunate tendency for coyness when faced with rejecting someone...but also that this is grown out of by our 20s, or at least I'd expect that to be the case with most.
It seems like the OP did make his romantic interest clear, after she canceled, that is. At first I can see how she may have thought it was just a friends hanging-out situation though. Maybe now she's confused, because maybe she had not considered romance a possibility before.
I admit I had (and probably have) a tendency to just let someone pursue me until I'm finally cornered & must give a clear response. I'll be vague, just to "see what happens" because I'm not disinterested enough to close the door totally (which I would do swiftly & clearly if I was disinterested). BUT, if I AM interested from the beginning, then I'm more likely to make that clear, especially in a situation such as this. It's this grey area where I'm not sure how I feel about someone that leads me to be ambiguous with them. I usually have
just enough curiosity to keep me from clearly turning them down. It's a Ne thing to be pulled in by "potential", and the slightest bit can keep you open to something enough to eventually be won over by it. This is the more passive version of the ENFP, who injects the potential & makes it develop themselves.
Between you & me & everyone else here

, you could probably exploit this aspect of INFPs. I'm pretty sure loads of INFPs end up with xSTJs because they doggedly pursue the INFP until she caves (more typical behavior of the xSTJ than xNTJ, IMO). You might not want to win someone over that way, but I think it's an option.... If she was really, really not interested in the tiniest bit, then I think that would be clear by now.
My personal experience with INTJs is just that... I'm curious about them, just enough to go out a few times, but if doesn't begin to develop beyond a curiosity (which it never has thus far), then I lose interest. You have to squeeze every ounce of potential & make it work for you, then you must make sure some of that potential begins to manifest as a real connection. Then you will have caught the elusive, ambiguous INFP
Please also keep in mind that the INFP is neither an extrovert nor a Fe type, and that you're not going to get openly flirty & gushy typical girl behavior. Every single guy I've ever dated has said something like, "I can't tell how you feel about me" within the first few weeks to month or so of dating. I probably seem very ice-queenish at first...that's just how it is. I'm slow to warm, and it seems this is not unusual for INFPs. However,
I see the contrast in myself with my usual behavior, and part of that is a willingness to make time/effort to see someone when I'd otherwise be content to not socialize.
Ok for curiosity's sake is there not a 3rd option of detaching and trying again in August? Assuming she is available. Or does that kind of thing just not happen
And about the self protection...what is she protecting? It's only a first date, not a romantic venue and involves an activity. I don't understand why she wouldn't wanna try if remotely interested. There is something to gain possibly, but what is there to lose? We OBVIOUSLY enjoy each other's company enough to be friends at the very least. She wouldn't have to open up if she didnt want to. And given the fact that summer break is coming up, any negative outcome would easily diffuse during that time frame
I generally think this is precisely what will motivate the typical INFP to go out with someone they are lukewarm about (as described above). I think a curiosity will generally conquer nervousness too, especially if it's not a total stranger. I wouldn't wait too long....just ask her when she's free again. I missed the point about waiting til August -
why? That's a bad plan, IMO; you need to play on her curiosity NOW.
It would really help if we knew her enneagram type. I do wonder if the 9, 6 & 5 type INFPs are possibly more guarded romantically than the 4, who I think is possibly the most risk-taking in romance. 9s seem like they fall faster though (?), but they may be passive about rejecting someone too (?). As a 4, I'm novelty-driven enough to have a "let's see what happens" attitude, but then have too high ideals that will make me lose interest shortly thereafter. 6s seem the most anxious/suspicious about the unknown. I'll over-analyze, but it tends to be positive speculation, imaging ridiculously good things. I rarely see "disaster". It's either interesting enough or not, and if it's interesting, then I think about how it could meet some ideal.