Give up immediately?
If a smaller company says they are not hiring at the moment, should you give up straight away or should you talk to your boss about the situation again to see if you still get a chance?
If the boss changes his mind, he can hire someone else.
The company will have its reasons why they have rejected you or have already occupied all positions.
Especially small companies don’t have it easy at the moment.
Try it somewhere else before you get no more place (I think for a training).