Preschool intro to building
The preschoolers are practicing shapes and learning to build. Usually a building challenge like this works for older kids, where they have to build the biggest tower they can. Trying to build anything was quite enough of a challenge for the 3-5 year olds, but they nevertheless built some cool little buildings.
In this case, I found it was useful to start the kids off with making a square with their clay and popsicle sticks flat down, and to have them add a straight-up stick after that. The motor skills and shape recognition here are a good level of excitement, and helps the kids discover how the clay holds sticks together.
From their, I gave them the task of connecting the top -- however they figured out a way to do this was fine, as you know, science and engineering isn't about right answers, it's about figuring out what works, how it works, and finding solutions!