I think those might actually be frosted glass cups.
Here is the best copy I could find, and the flared edges do not look like plastic cups - also the shiny inside and matte outside looks more like glass frosted on the outside.
PP was not in commercial use until 1957 (not sure when it was first used for cups), PET disposable cups weren’t a thing until the 70s. Disposable cups in the 50s would have been wax paper.
Fast film (you can see how grainy it is when you zoom in a little) and shooting in full bright sun = you can shoot very short exposure and freeze motion. There were already cameras in the 1930s with mechanical shutters that could do 1/500th and even 1/1000th of a second exposure, which is plenty fast for this type of shot.
The lens looks pretty fast too - depth of field is very shallow, although part of that is also due to possible use of medium or large format - faster lens (lower f stop) and larger film both allow more light capture, and therefore faster exposure as well, but at the cost of less depth of field.
Edit: here is a good print of the full frame - looks like ~1.50 ratio, so probably 35mm film (not medium or large format) - I can’t find a lot of information about what cameras Max Alpert used in the 30s, although he did use a 35mm Leica on at least some photos from that era. A Leica III could do 1/1000 in 1935 for example. The early Soviet cameras from the 1930s were also basically direct copies of Leicas. The frame also looks a bit underexposed, which could be due to pushing the exposure for more speed.