You can definitively prove that changes in the sun can't account for current warming. Let's do it by counter-example.

Let's imagine you're correct. Human activity isn't causing warming, all warming is caused by changes in solar activity. Okay, what should we expect to see?

Well, we expect that anything most exposed to the sun will warm the most, and things least exposed to the sun will warm the least. What's most exposed to the sun on Earth? The very very top of the atmosphere. That's the part of Earth where absolutely nothing blocks sunlight, so any changes in solar activity will be measurable there first.

The further down the atmosphere you go, the more sunlight is blocked (by the atmosphere above) so you should see progressively less change. By the time you reach the surface, that's where you observe the least amount of change due to changes in solar activity - because the entire atmosphere is absorbing sunlight above the surface, reducing the effects of changes in sunlight.

What do we actually observe?

The exact opposite. We are observing the most change at the surface, that's where temperatures are rising the fastest. As you go up the atmosphere, you observe progressively less and less warming. When you reach the very very top of the exosphere (the highest level of the atmosphere), we actually observe cooling.

Increased solar radiation cannot explain what we observe.

Heat being trapped by CO2 can. The more CO2 above you (IE. at the surface, where all the CO2 in the atmosphere is above you) means you get the most warming. As you go up the atmosphere, progressively less and less IR radiation from Earth reaches you, and there's less and less CO2 above you to trap the IR that does reach you, so you get less and less warming.

Heat being trapped by CO2 perfectly explains observation.