Why do you need more soil?
Is it to store
water, if you mulch you can slow down the evaporation rate thus you would have more water.
Also a lot of tree can grow with very little water (drought tolerant) so choose your species/cultivar wisely.
Do you want more soil to hold more nutrients?
Nitrogen in produce by living organism just make sure that 25%-40% of your garden in covered by Nitrogen fixers eg legumes.
Your bedrock is really just a huge store filled with mineral,
So as long as your plant's
roots(including symbiotic fungi) can make it down to it, they will get the minerals.
Fungus/mushrooms do a great job at using acids to dissolve the bedrock for mineral in exchange for sugar from the plant roots.
biomass does not really stick around in the soil for long esp new growth like what you are talking about.
You best bet would be
biochar. After creating the biochar maybe you can then mix it in in a 1 to 1 ratio.
But I am pretty sure that would negatively affect the plant.
Healthy soil is 25% water + 25% air +5% organic matter +45% minerals.
So the best way to increase the soil is to make it more porous so that it can hold more water and air.
Daikon radishes sound like a job plant for the job.