>>Would it be reasonable to observe a sparkler for 5 seconds, and then claim it has been burning for 100 years?<<
Actually with Doppler shifts we can tell the speed of stars.
With triangulation we can tell the distance to stars.
Using the speed of light we can tell how long the light had to travel to get here.
Putting all this together we can show that the light from some distant stars traveled a million years or more to get here.