I thought about using a noise node, and somehow randomize the noise's seed.
Can anyone help me?
I accidentally managed to make such shader while playing around with nodes. Here's how the whole setup looks:
We're using Gradient Noise node, but to animate it, we're using Rotate node that rotates its UV (rotating the generated noise texture), with Time node connected to Rotation value. However, if you crank up Rotate's Center parameter to 10,10 it doesn't look like it's rotating anymore. Gradient's Scale parameter has to be 90+, but not too much because it looks worse then.