I have spent some time thinking about this particular task on my to-do list of planting a trillion trees. With the increasing rates of carbon dioxide in the atmosphere on Earth, it's clear we could use more carbon sinks. Trees are a natural solution because they adapt to high co2 environments by growing larger. Meanwhile, people enjoy breathing oxygen which is a waste product of photosynthesis. Higher availability of oxygen probably contributes to why people are drawn to coastal areas. Being near sea level provides more temperate climates and higher oxygen concentrations due to increased atmospheric pressure. So, how to plant a trillion trees?
One problem is that it's common to focus on the planting aspect. One thought was to use robots to dig and plant. It's a fair idea, except it will take an estimated 100,000 robots to reach the goal. Another approach is to put seeds in a delivery device and distribute the seeds across a wide area. An example would be a drone with seed dropping device. The germination rate tends to below that of a well-managed seedling placed in an ideal location. This method also requires a species that can grow without any burial. Otherwise, the seeds would need to be encapsulated in soil.
The next idea is similar to other delivery methods except more grotesque. The basic idea is to use people as the delivery device. Some plants have evolved to entice birds to eat their seed-containing fruit and later poop out viable seeds that may germinate. I think food like blueberry muffin tops would work well because nobody wants to eat the bottom of the muffin anyways. This method is mostly for entertainment value though. This may work on a small scale but also suffers from some problems. This way requires species with genetics capable of surviving ingestion. Plus, with modern waste management, it seems like it isn't the best way forward.
The planting aspect is what people get caught up on when thinking about massive reforestation projects. One thing I have learned from tending to bonsai is that planting isn't needed. In some cases, there might be a pile of soil on a rock. The idea is to add a seedling to a biodegradable pot. Once it becomes hardened to local weather, it would be placed directly on the ground surface, where the roots will grow through the temporary pot and into the ground below. In this way, there is no planting needed. Egg cartons can be used for a biodegradable pot.
So then the problem becomes how to get a trillion seedlings? The solution is likely cloning. Seeds are also an option but take longer. Using a robot arm to clone trees could be an ideal solution. However, not all species are easy to clone. I've found some trees are borderline impossible to clone and others that are so vigorous, they can be cut and placed directly into the ground with zero treatment. However, the magic recipe to maximize clone yields is mostly about plant choice, substrate, mycorrhizal culture, and timing. The first aspect being the substrate. The most ideal one I've found yet is sphagnum moss. Inspired by the famous Peter Chan's way to air layer, the moss holds water very efficiently for cuttings as well. It provides a good mycorrhizal environment. However, it is a natural resource with limited quantities. Rockwoll or mineral wool is a good synthetic alternative except the fibers don't biodegrade and can be inhaled. The culture is a mycorrhizal start that inoculates the cloning environment with beneficial fungal components useful to many deciduous tree species. Using these methods it is possible to get very high propagation rates. Combining cloning, the automation of a robot arm, and a distribution method, I think it is possible to reach 1,000,000,000,000 trees.