Initial Color, and Color Over Life modules, only have an effect on particle appearance if a Particle Color node is used in the particle material. Since you don’t appear to be using it for something else, you can use an initial color module to select your SubUVs. Set initial color to Distribution Vector Uniform. You have 2 SubUVs in x and y, so set Min to 0,0,0 and Max to 2,2,0. Then set up your texture sampler like this.
Then you’ll get a random SubUV for each particle.
