I took a look at the example model that you attached to your question. I saw what you mean by the square pulse does not start at zero.
Fortunately, this is a simple fix. The Scope block, by default, limits the number of points on the scope to 5000. If we disable this, we can see the entire square wave as expected.
To disable this:
- Double click the Scope block to open it up
- Click the "Gear" icon in the Scope to open the Scope parameters
- Select the "History" tab
- Uncheck "Limit data points to last:" and apply the changes
Additionally, the reason you originally saw trapezoidal-like waveforms instead of square waves was due to the large step sizes used by the Simulink solver. Under the "Solver Configuration" parameters, you can specify a "Max step size" to make sure the solver always takes smaller steps.