I appear to have found the original version of a previously-posted photo of Temple Square c.1879, looking south from the NW corner of Temple and Main Streets. In this stereoscope view, you can see the top of the United States Hotel's four-storey-tall flag pole, which, for many years after the Civil War, was the tallest man-made object in Los Angeles.
Wikimedia Commons. (A high-res 2737x1446 version can be viewed here.)
Now, if you were to go up to the top of the Temple Block (at right in the above images) and look northward, this is what you would have seen. The building with the three cupolas was the Baker Block. The tall mast at right was not a flag pole, but an arc-lamp street light. (An excellent illustrated history of street lighting in Los Angeles can be found here.)
Wikimedia Commons. (A high-res 2737x1613 version can be viewed here.)