Yeah, she will believe in this. She’s already really insecure about her relationship, don’t need much incentive.
Even when you are insecure about a relationship, when a girl invite you to go bowling on your day off when she is in no case obligated to, there's no way you should believe that she can't stand your face. Else, why would she invite you to begin with ?
Plus, Mai been pretty forward about enjoying Tae's company from day one. I could understand if she sent mixed signal but she's not even using a lighthouse at this point, it's a freaking supernova.
Her begining that girl that just popped out of nowhere would be frankly stupid as writing go, there's no freaking buildup making it possible for Tae to think "oh yeah, that may be possible".
Frankly, I was expecting that girl to go "you looks like a pedo to me, I'm gonna report you if you don't stay away from Mai" as it would be much more logical for how the story been unveiling so far.