Fill a Data3DTexture with texels from a noiseshader

Questions
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1

the last few days have been quite exhausting but it was worth it. I now understand webgl2 shader much better.

now i face the next challenge. I want to create a 3D texture. With a shader I could use powerful noise functions. But the question that arises for me is the following: how do I get the texel datas from the shader, which are in the GPU, into my Data3DTexture?

maybe this pseudocode will help to better illustrate what I want

		//Values for the Data3DTexture
		const size = 128;
		const data = new Uint8Array( size * size * size );
		
		//---------------------------------------------------------------------------------------------
		// what I imagine is a shader which generates the texels for the Data3DTexture
		const FS =`
		
		in int size;	//x, y, z
		out vec4 Color;
		
		someNoisefunction(vec3 coord){
			...code...
		}
		
		void main(){
	
			ivec3 pixel = ivec3(gl_GlobalInvocationID.xyz); //something like that but i need a webgl2 equivalent
			Color = texelFetch(someNoisefunction(pixel), pixel);
			
		}`;
			
		data = reseive all texels from shader
		//---------------------------------------------------------------------------------------------
	
		//now create Data3DTexture 
		const texture = new THREE.Data3DTexture( data, size, size, size );

does anyone know of an example in which a Data3DTexture is filled using a shader?