SOLVED! Looks like this photo was most likely taken in the 5300 block of 53 Avenue in Long Island City near the Polaski Bridge. Thanks for the lead, @HeHe_AKWARD_HeHe.
I am back to see if the Reddit hive mind can help solve another New York photo mystery. My family has been curious about the photo's backstory for decades. I would be relieved if I could answer a few questions to help my family add context to the photo:
Where was his photo taken?
Is the elephant associated with the National Theatre Circus or the 1939 World's Fair (or possibly both)
Who is the well-dressed man on the left?
Here is what I know about the photo:
The gentleman leaning against the truck is my grandfather, Lloyd Charles Kirk. He owned and operated the truck during his time living and working in Manhattan between 1937-1942. He worked for The National Theatre during this time as well, which was noted on the back of this photo. The address of his transportation business shown on the side of the truck was in Greenwich Village
I have looked through the NYC tax photo archive of 1940 concentrating on the areas around many of the pencil marks on the atlas without finding any similar buildings seen in the background.
On the right side background of the photo appears to show a white smoketack-like structure.
Now let's talk about the elephant. I am assuming that the Asian elephant was associated with the National Theatre Circus, which was active in Manhattan at the time. The circus did have an Asian elephant named Japino or Rosie. The Library of Congress mentions that the elephant had once escaped its confines and accidentally returned to Barnum & Bailey. I wonder if this photo is related to that story? Perhaps this photo was taken when the elephant was handed off from B&B to the Fed Theatre? https://www.loc.gov/exhibits/federal-theatre-project/circus.html
Oh, and one more thing: welcome to my obsession. I hope you can help solve this mystery!