How can I find the CG of a model aircraft based on its dimensions?
You cannot.

Assuming that by 'dimensions' you mean the values for length, width and height, there is no way to calculate CofG from it. Two planes with exactly the same dimensions, but one with a thicker wings or tail, will have different C of G.

Even if you know the precise shape of the plane, the C of G cannot be calculated. Replacing a wooden tail with a heavier metal one with the same shape would shift the C of G. So would replacing the engine with a heavier one.

You need either the plane itself, or exact plans showing all the components and their weights (and a lot of maths).