Since the only constraint on the titanium is that there are '8 miles' of it, and the only constraint on its interaction with the cheese is that the cheese have 'enough force' to 'go through 8 miles of titanium,' the simple solution is to choose to assemble the titanium into a hollow cylinder, or 'tube' shape, eight miles long. By orienting the tube vertically on Earth's surface, the only force needed to put the cheese through it, would be that required to put the cheese at a point slightly above the top opening of the tube. Depending whether the total force measured includes construction of the tube, it might be more convenient to construct it underground or at a deep spot in the ocean, but it is physically possible.

To prevent the cheese from disintegrating, it would have to be accelerated very gradually. Unfortunately, cheese is not a topic of great interest in materials science, so its strength would have to be estimated from other materials. I suggest soft plastic or rubber. Regardless, cheese would certainly not survive the atmosphere any better than 1-gram pieces of rock known as meteorites or shooting stars, so the collision would certainly have to occur in space. But since even space is not a perfect void, containing 1 hydrogen molecule every few miles, the required gradual acceleration of cheese could not take place over a great enough distance to prevent breaking apart directly from acceleration, yet small enough to rule out annihilation by collision with a hydrogen molecule.