My car garage has a ramp and it has 3-1/2 inches of vertical step from the ramp. My car's ground clearance is 170mm which is 6-1/2 inches.
I think my car should get in and out using the ramp without any problem, but I'm worried that the vertical step might damage the car's tyre.
I'm willing to try some makeshift arrangement rather than doing something permanent, but I'm open to all ideas to solve the problem.
Firstly, that ledge will not damage your car's tires*. The impact of a tiny ledge in a highway at 70 mph (~110 kph) is many times more forceful than a slow roll over this ledge.
Then, the asphalt should've been sloped up to the concrete slab's level. That was a massive failure on the part of the contractor and should be corrected. At a minimum, any professional should've asked about the step before laying to that level.
Otherwise, consider several options:
Cold-pack asphalt to make a ramp about 18" (~45cm) long. This will work well but may not stay in place for the long term. You may need to replace it occasionally.
Install a steel plate, anchored to the concrete. Even a 12" (~30cm) wide band with a bend at the to level would do. You could anchor it with flat-head concrete screws.
Install a pressure-treated 2x6 (38x140) on the asphalt, tight to the concrete. By roughly halving the ledge into two separate ledges you dramatically reduce the bump you'll feel. Anchor it with expanding sleeve bolts into the asphalt.
Cut the asphalt back 18-24" (~45-60cm) and pour a concrete ramp. This is a somewhat advanced project from a DIY perspective, but is certainly feasible.
Grind or cut the concrete to create a short slope. This could be done with a variety of saws or grinding tools, depending on what's available. Even reducing the front face height by an inch (2.5cm) would be a big improvement.
*Assuming proper tire pressure and adequate remaining tread depth. Note that the proper tire pressure for a given vehicle is not on the tire--it's on a label somewhere on the vehicle, and that radial tire pressures are difficult to judge by eye. Tread depth should never be reduced beyond the molded indicators.
