While more feasible than the suggestion to move the planet further from the sun with a massive explosion, any project that would give Arthur C. Clarke's ghost a raging erection still presents a considerable engineering challenge. The BBC helpfully informs us that "By far the greatest challenge is getting the sunshade into outer space," which is like saying that the greatest challenge in becoming Spider-Man is getting spider-powers.
Part of the problem is that the heavier something is, the harder and more expensive it becomes to send into space. So, of course, the proposed solution is to slam a giant electromagnetic gun into the side of a mountain and fire the material into the cosmos to be assembled there, bringing the cost down to mere trillions of dollars. No, the technology doesn't exist yet, but what else do you think America is going to build in the future? A functional social safety net? Don't be absurd. If you're lucky they'll test the mountain gun by blasting food bank donations at Detroit.
There's also the cheap and boring option of merely shooting a bunch of sulfur into the atmosphere, probably with some dumb normal gun, to simulate the aftermath of a gigantic volcanic eruption. In terms of temperature control, this would probably work well as we have enough data on how volcanoes affect the global climate to adjust God's thermostat with considerable nuance. The real concern is that there would somehow be unintended consequences, like a few countries experiencing more climate problems even as the rest of the world benefits. Now, these are all theoretical, "break glass in case of imminent apocalypse" plans, meaning you probably won't see sunshades in the news anytime soon. But you for sure will see our new young adult trilogy about a climate war sparked by the eruption of an artificial mega-volcano.