At the press conference Elon said that all remaining tests are expected to be finished by the end of Q1 2020 and the first flight is expected to launch in Q2. Of course they have to analyze the data from today's test.

Also the flight can be delayed if NASA decides to extend astronauts' time on ISS which would require additional training for them.

I heard that the first flights are scheduled for first quarter 2020 if everything goes well today, which it from the first look did.