Use a diamond core bit and a power drill with a suitable clutch to avoid injury if the drill snatches - hire it/them if necessary.
Start by drilling a pilot hole all the way through. When drilling with the core bit, start from one side and then move to the other side when the pilot shaft emerges - that way you'll get a clean hole, and one that lines up.
That's all good, and will save money on tooling at the expense of labour and of quality of finish, but you still have the problem of keeping the perimeter of hole neat, so for this method I would do the stitch drilling half-way through from each side and then chisel out the less visible parts (if/where necessary).
Speaking as an ignorant amateur, in my early years i used to make holes in walls with rings of holes, hammer and chisel.
From the first time I hired a core drill, I would never go back. It's so easy I found myself going round the house looking for suitable places to make big holes (extractor fans, tumble drier, cooker hood)
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