I can't find very much on this, but I highly doubt it was expressway-related. The Crosstown was planned to extend south along Cicero from the Edens junction. This is two and a half miles away. It is more likely that it was a building involved in the manufacture of bricks. Then again, I can't find any proof.
Here is an article which mentions children on a large building around Brickyard, and a picture that may be this thing: http://www.forgottenchicago.com/b1.pdf
Also, this is an aerial photo of the Brickyard site in 1939: