We first see them interact in a flashback after Sarek and Amanda agreed to take in Michael and raise her Vulcan alongside Spock.
The young Vulcan doesn’t acknowledge her presence at first, choosing instead to focus on a drawing he was creating on a screen that made holographic images.
After some awkward introductions, Sarek and Amanda take her upstairs to meet Spock.
Eventually, he gets up, only to reject Burnham’s handshake and slam his bedroom door in her face.