The cave shown here (when he shoots the light arrow) is
deep.
That 3rd coordinate on the map is the Z depth, shown in previous trailers. Here it is reading
-0.479
In the previous trailer, you could see this rising as Link rides the rock up into the sky with rewind time -- and it didn't reach a positive number that large until he was all the way up in the sky island space.
So we have confirmation that the networks of caves go as deep underground Hyrule as the sky islands go above it.