As others have pointed out, it's theoretically, if not technically possible or feasible to shade the earth, but we are faced with the fact that most of our tech and accessible resources are inside of a large enough gravity well, that will likely continue to pull-in more material (~40Kt) per year than we will ever be able to launch, with current launch systems. But we can bootstrap the process:
You would only have to launch automated mining and manufacturing equipment to begin the process of building a self sustaining space economy that lives off of the material available in tiny gravity wells (asteroids/comets/Moon), and uses abundant solar energy to power it all. And most of what does get launched from earth, would have to be inserted into LEO by electromagnetic means (rail/coil guns. Elevators are presently off the menu).
We could probably build practical guns with current tech, that could place bulk materials into orbit, but they would subject their payloads to such extreme accelerations, that most assembled equipment and no human could survive. The bulk of the parts and raw materials could be launched that way, for assembly in orbit. But, since nothing below escape velocity can avoid falling back to earth, you'd have to have some space tugs out there, to intercept the payloads and move them into stable orbits.
The first hurdle would be to construct the guns, which would be nearly vertical structures built at high altitudes, and rising 20km or more. The longer the gun, the lower the mass of atmosphere, that the projectile must decelerate through, to be reachable by the tugs. Such a structure would have to be flexible and dynamically stabilized by a variety of means, including thrusters, which would also be needed for aiming.
While that's happening you need to get out to some carbon and ice bodies where you can make fuel. We can launch the first tugs and some fuel into orbit using rockets, but acquiring fuel off-world, would be the highest initial priority, to keep the tugs running. The tugs wont be able to use solar power for propulsion, because they will be entering the upper layers of the atmosphere, where solar panels would produce too much drag, and they are going to need a lot of thrust, so that means chemical propulsion. It's possible that a hydrocarbon based fuel could be a good choice, at least initially, as it might produce enough smog to temporarily cool the planet (TBD), but there's plenty of hydrogen and oxygen out there that can be produced using solar power, and those two elements would likely be the least environmentally damaging in the long run.
Next you launch a minimal number of assembly stations via rockets. These will be used to build more robotic stations as supplies arrive from the guns. They can use solar power and ion thrusters for maneuvering and stabilization.
When you get your orbital production levels high enough, you can start using some of it to build miners and transports. With those, you can get out to the metallic and rocky bodies to start mining the rest of what you need. At some point you will rely entirely on off-world resources and disassemble or mothball most of the earth-bound launch systems.
An alternative would be to use rockets to provision the surface of the moon with robotic miners and assembly systems. If you can produce Teflon and/or carbon fiber on the moon, then you can build space elevators there, greatly reducing the need for rocket fuel. Guns also work there, for launching large masses into space. Lacking an atmosphere, and having far less gravity, you can use guns to safely launch humans into space from the surface of the moon.
The moon is ideal, but to get there with enough equipment to bootstrap the process at a high enough rate to build your shield in time to prevent total collapse of the earth ecosystems, you'd still need to build some guns on earth, to deliver the initial equipment.
The current limit of human built vertical structures, is <1Km. The tallest buildings, use dynamic stabilization for human comfort and to prevent destructive oscillations, driven by the winds. The structures needed for rail or coil guns, would not in any way be built for human comfort, so their total mass/km would be a great deal lower than our current tallest buildings. I don't think it would be too much of a stretch to push the limit to ~2Km with current construction technologies. That's an order of magnitude lower than you'd need for a practical system, so we'd have to invest more in materials research and divert a larger fraction of our hydrocarbon production into making Teflon, graphene's, carbon fibers and other advanced materials.
It is likely that in the short run, you'd have to deploy some vertical thrust to keep the gun from collapsing. This could be provided by electrically driven fans. Rather than model the gun as a vertical spike, it would be more like a stiff rope or conduit, that could possible be leaned over/curved to some extreme angles (10 degrees maybe?) for aiming purposes. Some modeling of the atmospheric effects of operating such a structure for up to several decades, would be very important. Such a system would have it's own, local, small redundant nuclear power plants, in addition to being connected to the power grid, to ensure the structure doesn't collapse unintentionally.
The key economic benefit of using guns, even when they must be permanently supported by some thrusters, is in the avoidance of the rocket equation. You don't have to lift any fuel, to provide lift a second later. And electrically driven propulsion all around, is more environmentally safe. They are the only way we can bootstrap any kind of major push beyond our gravity well, without destroying the ozone.
Elevators to earth orbit, currently require the use of unobtanium. Graphene and carbon nanotubes have been ruled out, because they don't have the required tensile strength and those were the previous front runners.