This assumes that the only way a project like this could be pulled off would be for the state to open a "money firehose" and spray it onto buckets held by private corporations. Is there any reason it couldn't, in theory, be a state controlled venture? Especially for something as seemingly basic as "planting trees", I don't see where the corporate expertise comes in that the state could never replicate.

"The state will handle this" is not only a legitimate structure in totalitarian dictatorships, it's used across the developed western world for most public services.