Let's start with the actual example of the artificially generated desert that exists in the real world, called Błędowska Desert. There are some differences compared to your question but it can give you an idea what will happen since there is no change of the climate. As you can see now the dessert is slowly being grown over and that's what most likely will happen in your world's case. Since you do not change the elevation, the speed of this process most likely will be much faster since the conditions will be much more in favour of the flora restoration. So in 1 year the changes will be probably visible and in 5 year serious (for instance there'll be no longer purely-sand places), however most probably the forest will not be fully back in it's place. Also the increased amount of sand might change the type of initially dominating trees to those having more extensive roots system.
EDIT
I've missed the original forest line/elevation which means the processes of restoring the flora will be slow, especially initially. Also there are some springs since there are rivers starting in the affected area. We may expect those springs remain so the water supply remain provided, but the river beds will probably change (depending how deep the sand layer is). So the desert will be grown over from edges and plants will show in the areas most humid. Anyway changes within 5 years are going to be rather small and noticeable mostly in the areas where water can be found. In longer run (decades) the dessert will decay and eventually get completely overgrown. The rest of my answer remain fully valid.