What first aid treatment can one give to a vomiting 4 years old child without fever?
​When a child is vomiting, you cannot stop the vomiting if it has already started. Let the vomiting stop then clean up and wash the face and rinse the mouth. But you can only attempt to stop the vomiting if the child is feeling like or retching as if he's about to vomit. Some blow on the child or sprinkle water which may stop the retching from going to complete process of vomiting temporarily but most will still vomit anyway as long as the cause of the vomiting is not attended to.
The most important thing is to take the child to see a doctor for the underlying cause of the vomiting to be addressed.