It’s important to keep in mind that C is not just the speed of light but the speed of all electromagnetic radiation (EMR), from gamma rays and x-rays to microwaves, radio waves and electricity. A frequency range over 18 orders of magnitude. Visible light represents only a minute fraction of the EMR spectrum. Light has a maximum speed of 3 x 108 m/s in vacuo and can be slowed when passing through materials like glass or water.
The speed of light is not that fast, it takes light 8 minutes to travel from the sun to earth. Any animation that zooms in or out of the solar system (Big Bang Theory intro has one) is depicting greater than light speed. C is fewer orders of magnitude from personal experience compared to the universal distances or mass mentioned earlier. A bullet, a plane, the speed of sound and the earth’s rotation are all on the order of 102 m/s, six orders of magnitude from C. It’s not hard to imagine greater than light speed, nature just doesn’t allow it. What challenges the imagination is that C is both a speed limit and a constant. Constant speed that’s not relative to velocity of the source or observer is not intuitive and goes against what we normally observe*.

There has to be good reason that C is both constant and a limit, it suggests there is something in the nature of light that leads to this result. Einstein recognized the significance of the constancy of the speed of light and it led to his special theory of relativity. In order to resolve a constant C he needed time, distance and mass to become flexible. As matter approaches C, length in the direction of travel becomes longer, mass increases and time becomes shorter. Our senses and personal experience make this a challenge to imagine.
*If you were driving the James Bond car at 100 mph and used the machine guns behind the headlights, the bullets would be traveling bullet speed plus the 100 mph of the car. If you turn on the headlights the light always travels at C independent of the speed of the car, forward or backward, and for all observers, the DB5, the target vehicle or someone by the side of the road.