Getting More Realistic Oscillatory Behavior with FET Modeling in LTspice
LTspice should be able to reproduce the transitory MOSFET oscillation just fine as long as the circuit model is reasonably correct. The rule of thumb for stray inductance is about 10nH per centimeter, so throw out all the strays from your schematic and start over as follows.
Add 5nH directly in series with each MOSFET terminal to represent the lead inductance. Add 100nH in series with the 50 ohm drive to the gate to account for your poor layout (as needed). Add 20nH in series with the small leaded capacitors. You also could add 5pF to ground from the junction of the 100nH drive and 5nH gate lead inductance.
Now you should see the oscillation. Note that the exact values given above don't matter unless you wish to match exactly the frequency and amplitude of the oscillation. If this circuit were running from a higher drain voltage, the oscillation would be large enough to rupture the gate and destroy the device (try increasing the power supply to 25 volts and see what happens).
The standard cure for this problem is to insert a damping resistance in series with the drain-to-gate capacitor that has a value equal to or somewhat less than the gate drive resistor (20 to 50 ohms in this case).