The cool filament in a bulb that has been off has lower resistance than the heated filament of a bulb that has been on for some time.
Work Step by Step
Before an “old-fashioned” lightbulb is turned on, the filament is cool and has a relatively low resistance compared to when it is hot (the resistivity rises with temperature). So, when electricity is first applied, the low R means a spike in current, and in power. This can heat up and vaporize the filament, ending the bulb’s life. When the bulb has been on for a few seconds, the filament has reached its final high temperature, with a high resistance and a steady low current. There is little thermal stress on the filament and the bulb is less likely to die under these conditions.