You do realize that there is no solid land over the North Pole, right? There’s ice floating on the ocean, and the ice sheet moves around as it floats. Underneath the ice there is the ocean.
Therefore, to drill into the North Pole you could just drill a hole through the ice until you hit water, or go to the bottom of the ocean and start drilling on the ocean floor.
There’s no specific reason to do so, however, and doing so would be pretty fruitless.
The North Pole has been reached by walking, by ice-breaker ship and by airplane. In the image below, a woman traveling on the Russian nuclear icebreaker Yamal holds a sign marking the North Pole, however, because the ice drifts, the sign also drifted away from the pole.
Sadly, there’s no Santa at the North Pole.