One source reported that Platt's Hall opened in 1860. Jack Tillmany reports that the first newspaper accounts of events there that he found were in July 1862. The building was on the NE corner of Montgomery and Bush.

It's listed in an 1882 "Guidebook and Street Manual." It was still operating as late as 1885. The Mills Building was later on the site.

http://sanfranciscotheatres.blogspot.com/2019/01/platts-hall.html

From Explanatory Notes:   This building on Mission Street, erected in 1866 and dedicated on 6 January 1867, was described as “an elegant brick structure, in the Anglo-Norman style, the auditorium of which is in the form of an ellipse, with a concave roof, which gives it a peculiar appearance” (Langley 1867, 15, 659).