By measurement. It was about 20 years ago, so the details are hazy but the experiment is simple. Put a solenoid coil around one end of a steel bar -say a meter long. Energise the coil to create a short powerful pulse. At the other end of the bar you have a sensor- another coil. When the far end of the steel bar becomes magnetised the coil detects the flux and creates a current pulse. Both input pulse and output are measured using an oscilloscope. I cannot remember the lag figure, but it was clear and unambiguous.
Let's understand each other... You write about "electromagnet"... I wrote about permanent magnets... And that's what interests me - I'm interested in how this different FORCE is generated?