Understanding Mosfet simulation and initial conditions in Spice
How can we explain that?


Actually it's the parasitic drain source capacitance that is inside the MOSFET that is producing the pulse at the output. Nothing really to do with conventional MOSFET action.

The FDC5614P has an internal capacitance of 90 pF and the CR time with R3 is 90 ns. At 5x CR the transient waveform should be pretty much over so that is a time of about 0.5 us and this looks about right on your graph given that you have a scale granularity of 2 us and my powers of interpolation aint that good!

Try shorting gate and source and removing C1 and R2 and repeat the experiment. I bet it looks very similar.