GodotBeliever This is trivial. The shader is needed only to interpret texture as alpha. Afaik there is no straightforward way to do this directly in a standard material with a procedural noise as it outputs alpha as fully opaque. There's a "trick" though using msdf.

Assign a noise texture to standard material's Albedo, enable Texture MSDF in material's Albedo section. In material's Transparency section set Transparency to "Alpha Scissor" and adjust "Alpha Scissor Threshold"

It can be done without enabling MSDF for a standard rgba file texture as that texture's alpha will be interpreted as transparency by the material.

For completeness, hare's the shader too:

shader_type spatial;
uniform sampler2D noise;
uniform float threshold;

void fragment(){
	ALPHA = texture(noise, UV + TIME*.2).r;
	ALPHA_SCISSOR_THRESHOLD = threshold;
}