S2 Nate goes into the restaurant and gets shunned by Jade. She refuses to sit him at the window seat.
S3 Nate walks in and she still doesn’t know who he is. She likely does not follow sports. She doesn’t find out who he is until her boss gushes over Nate.
Nate then brings a supermodel to the restaurant and gets utterly embarrassed. Jade watches this happen and she sits down with him.
Then we get the montage of Nate always walking by the restaurant and waving at her.
Next is the story from Nate’s mom about how his dad asked her out. Nate creates the elementary school project and goes to give it to Jade but ultimately falls flat on his face in front of her. He still manages to ask her out.
That brings us to present day where they are currently dating. Present day, however, is at least weeks in the future as the beginning of this episode had Richmond winning multiple games in a row. Those don’t happen all in one week. So yes it is very realistic and plausible that after weeks of dating Jade has started to fall in love with Nate.