You would have to bring in enough carbon for the initial setup. Once you have enough material to grow the first crop, you will decompose previous crops to provi

You would have to bring in enough carbon for the initial setup. Once you have enough material to grow the first crop, you will decompose previous crops to provide carbon and other nutrients for subsequent crops. In a closed system, none of that is being destroyed. In a real system you will get some losses (absorbtion by structural materials, population growth, leaks, etc) but these would be small compared to the overall amount, and easily made up with resupply at first and mined material over the long term.