You do not build a rainforest in a desert, you build a densely populated region with lots of agricultural land and some forests, so that people living there take care of enriching the soil and making sure that nothing collapses.
To do that we need to learn how to control the weather. There are multiple possible ways, like using mirrors in space, using large number of aerostats to change reflectivity, and to guide clouds to the place we need, solar updraft towers to inject dust from lower layers of the atmosphere into higher layers to form clouds, etc. Many of these are may not work, and many won't be cheap, but they will give us more control over the environment and will enable more people to live.
To do that we need to learn how to control the weather. There are multiple possible ways, like using mirrors in space, using large number of aerostats to change reflectivity, and to guide clouds to the place we need, solar updraft towers to inject dust from lower layers of the atmosphere into higher layers to form clouds, etc. Many of these are may not work, and many won't be cheap, but they will give us more control over the environment and will enable more people to live.