The switch launches a change through the whole circuit

A lamp does not wait for an electron to travel all the way from the power source. When the switch closes, it changes the electromagnetic field around the circuit. That change spreads along the wires, prompting electrons already present throughout the circuit to begin moving. Near the lamp, those electrons can start responding long before any particular electron from the source could reach it.

The signal moves through fields, not a stream of fast electrons

Copper contains mobile electrons, but their average drift—their slow net motion in one direction—is usually far slower than the electrical signal. The signal is a traveling change in electric and magnetic fields, which transfers energy along the circuit and nudges local electrons into motion. It is more like a coordinated push passing through a crowded line than one person racing from one end to the other.

The signal’s speed is close to the speed of light, but not always equal to it: the wire’s surroundings and insulation affect how quickly the fields propagate. Even so, the delay across an ordinary room-sized circuit is tiny, so the lamp appears to respond at once.

Why the distinction matters

The electrons do not need to make a rapid trip from the source to deliver energy. They are already in the wire; the changing fields carry the influence that sets them moving. That is why a lamp can light almost immediately even though the electrons’ slow drift would take far longer to cover the same distance.