Light from the earliest epoch of the universe has been traveling toward us for billions of years. On its way, it passes by enormous galaxy clusters. Their gravity slightly bends this light, just as a shop window distorts the view of the street behind it. As clusters grow, the bending becomes more noticeable. This effect is known as the Rees-Sciama effect.
Astronomers compared how well different future telescopes could detect such bending. The CMB-HD project came out on top: it would see the effect even with modest expectations for the instrument. Galaxy maps would also help, but less so. Maps of distorted galaxy shapes (cosmic shear) are almost useless: noise gets in the way.
Bottom line: detecting the bending of light by growing clusters is feasible. But weighing neutrinos this way won't happen in the coming decades.
The cosmic microwave background is light that began its journey when the universe was just 380,000 years old.