I have found several movies that show the WTC towers under construction. But in those movies, the towers were already pretty tall. I decided that there must be other movies with even shorter towers. I recently found What's a Nice Girl Like You? from 1971 that shows a fairly short tower under construction with the rusty red steel beams rising from the ground.
Next, I found what must be the earliest movie out there! It is a horrible movie called Putney Swope from 1969. There is an aerial view of lower Manhattan that shows a very short North tower under construction. It can't be more than a few stories high. The South tower has not even begun construction. Below is a side by side comparison of the shot from the movie compared with Google Earth. I have marked the diagonal corner by City Hall in green, St Paul's chapel in yellow and the North tower in red.
that's definitely one of the towers.. really cool.. please could you upload a screen shot from What's a Nice Girl Like You?. i'm really fascinated by the earliest ones.