Gefen,
My story is the opposite. A guy I went out with sent me a huge bouquet after one of the first dates. I freaked out. It was way too soon, and it did not make a good impression. My parents got more excited than me and it made me feel pressured.
No flowers, yet. Anything you send will send the message that you’re interested. I’d wait till sukkos, when you’ll have another week and a half to meet once or twice more, then send something (candy or fruit) platter as a general gesture of good will to the family for the chag.