Produce a kg of hydrogen using the sun, and this is 33KWhrs of heat energy removed from the energy of the sun, regardless of efficiency.

Which part of that do you not understand?

Are plants not actually creating, is this what you think?

When oil was formed on the planet, did this not reduce entropy? Did we not just convert it back to heat by consuming it?

I'll say it again, we can only create using the energy of the sun.

We can't create using any energy from the planet at all, never, all use of it raises temperature.

We are not looking to lower the temperature by an infinite amount, so why do you think an infinite amount of storage would be required?