The water that flows in the form of rivers originates from the seas and oceans. Water evaporates from the seas and oceans due to the heat from the sun and clouds are formed. When the temperature is right the vapor in the clouds is precipitated as rain or snow. This creates glaciers from which many rivers originate or falls on the land creating small water channels which gradually link up and form rivers.
There is no increase in the water level of oceans as the process of evaporation of water and the inflow of water from rivers goes on at the same time. Even if there is a net difference in the rates of the two, the volume of water in the oceans is so large that a small excess or deficit will not create a noticeable difference in their level.