Having visited the Müggelturm fairly recently, I was quite excited to see this picture of it by Günter Bittner, as I'd almost forgotten I had it. It appears to be from the 1960s, but the question is exactly when in the 1960s. Looking at the details throws up more questions than it answers.
The picture is a print on 6x4" paper. Unfortunately, it's matte finish, which is a real pain to scan, as it makes the shadows go all speckly. Still, that's not going to stop us taking a closer look...
Some of the things in the picture really beg the question of exactly what's going on here. There's a large cement mixer in the foreground, with a large and disorderly pile of bricks around it. Precisely what the bricks are for is harder to make out, as I can't see anything in the picture that looks like it's being built.
Next to the bricks is a pile of other building materials - it's hard to make out exactly what (slabs and panels of some kind), but I notice there's a GDR-standard manhole cover among them.
The manhole cover in particular suggests to me that this is more a case of serious initial building work than, say, repairs later in the tower's life. That said, the pile of bricks is very disorderly - more like something being demolished than bricks carefully lined up for use.
The fact that building work is going on might suggest that it's before its official opening, yet there seem to be a lot of people around it doing something. There are even tables out on the terrace, with people sitting at some of them, and people are up the tower too.
The caption to an image in the German Federal Archive (unfortunately not visible online, unlike a lot of the Bundesarchiv's images) notes that it was planned to have the tower and café open for the GDR's 12th anniversary on October 7th 1961. They didn't quite manage that, as the official opening wasn't until December 31st, but it does suggest that the building could have been nearing completion, at least on the outside, by October of that year.
The leaves on the trees mean it can't be December - though I've seen the trees in the Tiergarten keep some yellow leaves into early December, the leaves here look like they're probably green. The sun also seems to be too high in the sky for it to be winter.
The tree by the steps is around about the same size as it is in Bundesarchiv pictures from early 1962 this one for example), so it must be roughly around the same time. I can also find no evidence that building work continued into 1962, which would point to this being pre-December 1961, but I'd be very interested to see if anyone else has evidence that can either confirm or disprove this!
A lot of the people in the group in the foreground seem quite young, which makes me wonder if it's a school party. An outing to see round the as yet unfinished Müggelturm, perhaps?
Everything I've read seems to point to the tower and café only opening on December 31st 1961, so it's quite possible that this is 1962, but then comes the question of what's being built. If we decide, however, that this is pre-opening, there comes the question of why the café tables are out. A mystery indeed...if anyone has any answers, I'll be interested to know!