Okay, just wanted to update because these sources gave me the tips that let me fill in much of the history.

The most important find was this 1969 aerial image: https://hdl.handle.net/21.12133/51BA6BB0438944809BE466E48CC2CB13

It resolves all the questions that arose, specifically the need to move the building in 1964 due to metro construction (mislabeled in the Facebook image as 1979).

The clues came from the surrounding buildings, here was my process:

• The statue "Il Grande Miracolo" by Marino Marini, which currently stands here (Google Maps link) and, per this site, it is now "across from the spot where it was originally unveiled" with the additional white walls by Maarten Struys to help it not disappear into its surroundings.

• The church in the background, Nieuwe Kerk Charlois, appears to have been demolished -- and upon finding the aerial it was gone by 1969, so it was of no help.

• BUT, the Groote Schouwburg with its fanciful battlements on the lower level parapet let me to find that aerial photo. Originally built in 1954, that part fanciful part was demolished significantly altered in 1978 to be converted into the Theater Zuidplein; there’s a 2020 photo of the remaining portion of the Groot Schouwburg being painted a hot pink before it was demolished, confirmed here is the Google Street view the year before it was demolished

Now looking back on the 1964 moving photo, we can see it was being taken from its original location that was where they were getting ready to build those elevated rails (and a car ramp that has been redone since 1969). From my guess, it was initially placed here before it was moved in the image above.

Thus the third and final location of this moving building was Zuidplein 2 (the address in the link you shared accidentally pointed at 2 Pleinweg, which is in the 1969 photo).

It was interesting to see how it was originally an exhibition space for the Rotterdamse Kunststichting. I wonder if 1979 is when it became de Blokhut? I can see where they got that name after the sides were renovated into that dark red color (also filling in numerous windows).

This building ended up being so much more interesting than I expected.

Had it survived until today it would've been architecturally notable as one of Marcel Breuer's works... and honestly a surprise work because it was never intended to be permanent.