Tunnel boring machines that use high heat to melt through earth and rock have existed since at least the early 1970s. They were developed at Los Alamos. They leave no dirt or rubble to haul away as the molten rock is pressed into the surrounding tunnel walls.
And, I don't know why you'd need "a huge entrance large enough for a space ship."
I think they can probably find someplace else to park them.
"...the larger the facility the more people you need and the less secrecy can be maintained..."
Well, the US military manages to keep secrets pretty well and they have quite a large staff, I'm told.
As for needing roads ... the rumor is that there is a large network of tunnels that stretch beneath the entire country fitted with mag-lev trains so I don't think surface roads would be needed either.