Science doesn't say that there is no God. Science tells us about physical things, things which we can observe with our physical senses (such as sight), for example: stars, electricity, orbits, reptiles, atoms, chemicals, galaxies, forces, cells, lead, magnetism, electrons, gravity, tin, energy, protons, black holes, alloys, molecules, birds, gold, proteins, neutrons, heat. Science only deals with these kinds of things. It's not intended for or cut out for addressing things that are spiritually discerned, such as God.
You're right about that: science can't disprove God.