I looked at those directions again and it actually starts with two complete strips sewn together and then you cut them into sections that would make up the center square and the first strip.
Look at the directions to see what I mean. Absolutely doesn't mean that you can't take the 1 1/2" square you have and a 1 1/2" strip and sew all the squares onto the strip then cut them apart.
One thing I would mention is to definately use a ruler to cut them apart as advised in the directions. I was doing some small ones and to save time I just used scissors and cut them. The blocks were a little wonky but that was OK because I was trimming them down anyway to my finished size.