Some ideas already posted on IdeaSpies that should help win the prize by stimulating more ideas....

https://www.ideaspies.com/search?q=carbon+removal

https://www.ideaspies.com/search?q=remove+carbon

All good except in respect of CCS, a concept which has been found to be unviable and too expensive. Most experts are now reinforcing the importance of moving the focus away from repurposing the use of CO2 to strategies that drastically reduce its production in the first place. Nonetheless, some of the biotechnological approaches when applied across large and suitable areas of land do offer some useful promise. The Chines have developed a process that captures CO2 from smokestacks in existing power stations to produce algae which can then be utilised as a feedstock for farm use purposes.

May be a CSIRO based team might form the basis of an Australian entrant for this prize.

There is a simple solution - if the air is cooled to below -78.3 ° C using several series-connected Ranque-Hilsch Effect vortex tubes (each down to -50 ° C), carbon dioxide will fall like snow at the “cold” end of the last tube. It can be collected and disposed of in plastic containers (made from garbage), or decomposed into pure carbon and oxygen, or made rocket fuel. If installed in Antarctica (or lift on a balloon), then just one step is enough and use only the force of the wind without any energy consumption at all. Performance is high. Any scale. No consumables. Why do you need a competition if any engineer can now make it in 1 day? :)))