Yes, Landa knew who Shosanna was at that time. The key hint is in the question he claims to have forgotten to ask.
Landa is the Jew Hunter. He is portrayed as someone who finds everyone he sets his mind to finding, as someone who is very good at his job, at sniffing out every lie and enjoying it. He proves he has already done investigations into Shosanna by asking about her projectionist, so the only real question is how much else he already knows.
The key hint that he knows Shosanna is in the question he admits to have "forgotten" to ask, and which "must not have been important", the first of which is a straight lie, and the second of which is technically the truth, in a cruel way. It's not important because he knows the answer already.
In truth, he knows exactly what question he would have asked, if it had been a normal interrogation of an unknown person. In the Nazi ideology, and for the Jew Hunter in particular, nothing is more important than heritage in determining who is a Jew or not. He diligently inquires about her aunt and uncle when she mentions them, what their names are, what they are doing now. And with all that prompting, he conveniently forgets to ask the most natural question of all:
Who are your parents?
This is so far out of character for Landa that the only reasonable conclusion is that he did not forget the question, that he deliberately did not ask it because he already knows the answer, and thus, who Shosanna is.
He doesn't ask the question because he doesn't want to spook Shoshanna more than he already does. He does not want to press her for a (no doubt prepared) lie about her parents, like he will press von Hammersmark before the film's climax, or even be forced to arrest her on the spot in order to not compromise himself. He simply doesn't want to push her anywhere near a lie.
And yet he can't help but enjoy the little game he's playing with Shosanna (and for our, the viewers', benefit), by dropping hints that he knows: ordering milk for her, by being exceptionally jovial in what is a life-or-death situation for Shosanna, by meaningfully extinguishing the cigarette butt in the cream.
That also means he's already been planning to betray his country for his own advantage at that point, and is only looking for a real opportunity. He recognizes the cinema as that opportunity for acquiring the ultimate bargaining chip with the Allied command. That requires letting Shosanna off the hook and giving the go-ahead for the movie night.