The open space available within soil and rock is not infinite and is not constant from place to place or as you go deeper into the earth. Surface water bodies are basically locations where the open space below is completely filled. In effect, in reality, the water table intersects with the surface (the “lake” of groundwater is filled to overflowing).
In some situations, river flow can be faster than infiltration (rate of sinking of water into the ground) and the river or its destination lake or pond can be “perched” (getting water across the surface faster than the ground fills up), sitting above the groundwater level, but usually the situation is the opposite, where the ground is saturated, all open space is filled with water right up until the surface.
If you have ever been to the beach, a lake or the ocean, does not much matter, and dug a hole in the beach itself, you must have noticed that the underground is filled with water to about the very same level as the nearby lake or ocean. The water levels are linked, and essentially the same in close proximity to the surface water body. The only real question is whether water is flowing TOWARD the water body (acting like an underground river in a way, and dumping water into the hole that is the surface of the ground) or doing the opposite, and seeing water from the lake or river or whatever adding to the nearby groundwater and raising its level locally.
Reality is a bit more complicated than this story, because the ground interferes with water movement, so sometimes the flow is so slow through the ground that it is effectively impermeable and you get perched water bodies above the local groundwater level (kind of like a puddle on the surface of a solid rock outcrop, with no way to flow into the ground, but on a bigger scale).
The earth, though, is pretty much water-saturated from a short distance below ground surface to as far down as there is open space where water can get. Basically, there is so much water on this planet that the inside of the earth cannot come even remotely close to holding it all.
Although depths to groundwater table surface (where saturation is complete) can vary a lot from place to place, it is generally only a few meters or so down to that level, to the top of the water table, although many tens of meters is the situation some places. Mostly, though, at least in any reasonably wet region, it will only be a few meters down until you hit groundwater. This is why houses have French Drains and sump pumps. The basement bottoms are very close to the water table, and water table will rise and fall a bit (a few feet or a meter or two, perhaps, depending on climate) over the course of the year, so perhaps in spring you would get a flooded basement if you did not have the sump and drains.
How deep does the water table go? That was a point of argument in geology for a very long time, with the favored view being that groundwater that can migrate being absent after a couple kilometers or so, meaning that the inside of the earth was “impermeable” (lacking open space that water could flow through). Deep drilling has proven this to be false. Fractures exist even at many km down below. The water down that far tends to be quite hot, though.
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