Special relativity

I was listening to https://www.weltderphysik.de/mediathek/podcast/spezielle-relativitaetstheorie/ and it reminded me about the first time I really understood the reasoning behind special relativity. Einstein considered a mirror in a vehicle. If the vehicle is stationary, then light travels away from me at the speed of light, hits the mirror and comes back. When the car is moving, it becomes more problematic. Surely the light must have to travel faster than the accepted speed of light to overtake the car and reach the mirror. Einstein was aware that this would break the laws of electromagnetism as set out by James Clerk Maxwell. So perhaps the light wouldn't reach the mirror and you wouldn't be able to see the reflection. But this would mean that there would be a difference between sitting still and travelling at a constant speed, thus breaking Newton's First Law. To avoid breaking any laws of Physics, Einstein had to allow time to stretch and distances to shrink to bring the distance/time calculation back to the normal speed of light.