Where is the beginning of the river?

If you go up the river from the sea to see the beginning of the river, the width of the river narrows, and finally you reach a place where spring water spouts from the ground.

That place is called the headwaters, the headwaters can be a swamp or a lake.

The upper reaches of the river are very narrow. However, the width of the river becomes considerably wider downstream by merging with a tributary or being poured rainwater.

The source of spring water is rain and snow.
Rain and snow that fall on the ground soak into the soil.
The soaked water accumulates between soil, rocks and sand and becomes groundwater.
Groundwater flows into lower place in the ground and springs up when there is a gap above the ground.
Even if it doesn't rain, the groundwater will not run out suddenly.
Therefore, even if the water of the river continues to flow into the sea, the water will not run out from the river.