It would be unusual to diagnose FAS at birth, however full blown FAS is unusual, you can get some other symptoms.
Here is a list of full symptoms but would usually be diagnosed later.
low birth weight
small head circumference
failure to thrive
developmental delay
organ dysfunction
facial abnormalities, including smaller eye openings, flattened cheekbones, and indistinct philtrum (an underdeveloped groove between the nose and the upper lip)
epilepsy
poor coordination/fine motor skills
poor socialization skills, such as difficulty building and maintaining friendships and relating to groups
lack of imagination or curiosity
learning difficulties, including poor memory, inability to understand concepts such as time and money, poor language comprehension, poor problem-solving skills
behavioral problems, including hyperactivity, inability to concentrate, social withdrawal, stubbornness, impulsiveness, and anxiety
These tend to get worse as children age.