Interestingly no timelines yet, Samsung is handling this just as they did for Pie. But it looks like we are getting the 2nd version.
The update could be released tomorrow, when the One UI 2.0 beta program debuts for the Galaxy Note 10 and Note 10+ and the Galaxy S10 beta program is expanded to more markets. The markets in the second phase — Poland, France, Spain, the UK, India, and China — are likely to get the second beta update as the first release, although that is just speculation based on how Samsung tackled the Android Pie beta last year. It’s also not guaranteed that the second beta update will arrive tomorrow, but it should certainly be out before the end of the week.