Is there any sound API that renders sound similar to directx?

making an analogy, rendering 60 frames per second by calling a render() function 60 times per second will be rendering 48000 samples per second by calling the render() function 48000 times per second

In DirectX such voice rendering is made by a real-time thread which is running implicitly.
(in WASAPI, DirectSound, XAudio2)
You do not have to develop your own loop.
For example, a different API would be Open AL.

I am not sure of what you are asking exactly.

Do you want the sound to render 48000 times per second or is this what you are trying to avoid?

As kubera said, the sound gets played in its own thread anyway.