Well if we are being completely theoretical, i do think Germany had, sadly, a very large workforce at hand. Say, they smuggle 2500 Jewish prisoners to
the arctic. That is a very small number compared to the total toll of deaths, and easily hidden in the mess the Nazi`s left behind.
So, workforce is covered.
Onwards to the drilling operation itself!
What if they found a natural "cave" in the ice, built a ramshackle shelter at the opening, and drilled from there?
Such as:
I would imagine that solution to offer some shelter?
I really do not know how one would keep drilling the ice in the magnitude described, but surely mankind has done impossible things before.
Last, if i am to be completely, and absolutely mindbogglingly open minded, the food and water supply is next.
Water can be extracted. This we already know.
For the foodstuffs, i would imagine fish to be a viable solution?
Perhaps even seaweeds and other oceanic plantlife.
And no, just to be clear, i do not think there IS a base there. Merely trying too see if i my mind can fathom if it`s even possible.