There are several ambitious, "pie-in-the-sky" ideas that have been proposed as potential solutions to climate change. However, these are generally considered speculative and should be approached with caution, as they might have unintended side effects. The scientific community generally agrees that the most effective approach to combating climate change is through reducing greenhouse gas emissions, increasing energy efficiency, and transitioning to renewable energy sources. Here are some speculative, innovative, and ambitious solutions:

Geoengineering: This involves large-scale intervention in the Earth's natural systems to counteract climate change. For example, Solar Radiation Management (SRM) techniques, such as injecting aerosols into the stratosphere, aim to reflect a small proportion of the Sun's light back into space.

Carbon Capture and Storage (CCS): While already in use to some extent, the idea of deploying CCS at a global scale to remove large amounts of CO2 from the atmosphere is still largely theoretical due to economic and logistic constraints.
Space-based Solar Power: Collecting solar power in space, where the sun always shines, and beaming it back to Earth could provide a virtually unlimited supply of clean energy. However, the costs and technological challenges of deploying and maintaining such a system are considerable.
Building with Biochar: Biochar is a carbon-rich form of charcoal that, when mixed with soil, can sequester carbon for hundreds or even thousands of years.
Direct Air Capture: High-tech machines that act like trees, absorbing carbon dioxide directly from the atmosphere, could be a solution if they can be made economically viable and powered by renewable energy.
Nuclear Fusion: If we can make it work, fusion could provide a virtually unlimited supply of power with minimal environmental impact. The challenge is, it's been a few decades away for many decades.
These ideas are ambitious and could have significant effects on climate change if they were implemented and effective. However, each of them comes with significant challenges and potential drawbacks, and many are still unproven at the necessary scale. It is likely that a combination of many different approaches will be needed to effectively combat climate change.