When a train starts, the head of a standing passenger seems to be pushed
When the train starts it has a force pushing it forward, so it comes to motion immediately. Whereas your head is still in the state of rest and there is no force acting on it instantly so it tries to be at rest.
Now if you draw the sketch of the scene with coordinate axis
You will see that with reference to ground frame train moves forward but head tries to be at rest at origin as 1st law states, no net force so no change in state.
You notice the guy getting incline. Do you know why?
Yes absolutely because his legs are in contact with the trains floor which are trying to move him forward