Norderoogsand has sprung up from beneath the sea like a kraken of sand. It has since become home to 50 plant species and a bunch of sea birds.
Once a moss organism dies it decomposes into compost, adding organic matter to the sandy soil. This organic matter - or humus - contains carbon, nitrogen, and other essential elements. Birds drop guano containing further essential elements and ions such as calcium, potassium, sulphates and phosphates.
Over time, the soil becomes rich enough to support more complex plants. The seeds for such plants are also carried over in the stomachs of birds. These plants have deeper and stronger root systems which will help bind the deeper layers of the soil. When they die, their roots will decompose and leave humus in the deeper layers. Eventually this process will clear the way for shrubs to take hold.
There is a selective pressure here. A selective pressure is a natural force which says "A can live here but B cannot". In this case it is the salt water. Sand doesn't hold rainwater very well by itself, so for now all the moisture is seawater. Only those plant which thrive on beaches or in areas with high salinity will be able to live on Norderoogsand in the early stages. Once the soil is rich enough in deep humus to support shrubs it should also be absorbent enough to retain rainwater. Even so, it will still be quite saline. Coastal shrubs will be best adapted to these conditions.
The potential for trees to grow on Norderoogsand is uncertain. Soil that sandy might not hold a tree firmly enough. Deposits of lime from bird droppings will gradually improve the soil structure. Clay would make a nice addition, but it will not arrive there by itself. If sufficient generations of plants live, reproduce, die and decompose that peat has a chance to form then that is perhaps the best chance we have of seeing trees arrive on Norderoogsand.
Higher land animals are highly unlikely until the ground is very very stable and the plantlife is sufficiently fecund. Likely it'll just be birds and amphibians until the trees appear.
Alternately, the island could be helped along. A little clay, a little peat, a couple bay trees and this island would be halfway toward a climax community. This won't happen though. Biologists and geologists will argue - and rightly so - that Norderoogsand should be left alone to be observed. Primary succession is a rare occurrence, so the data which can be gained by watching it happen from scratch is scientifically invaluable. It can tell us something about our world that we do not yet know. The process of succession is slow, but when seen from end to end is a miracle of nature. I urge you to keep an eye on it.
I wish I was there...