Based on a character analysis of the protagonist, George Willard is probably nineteen years old.
This can be concluded through various statements in the text,
"George Willard, the Ohio village boy, was fast growing into manhood"
According to the psychology of stage of life, adolescence is the transition from childhood to adulthood or manhood in the age from 12 to 20 years.
Such transition has many implications on an individual related to emotional, social and vocational life. Similarly, such implications are also faced by the protagonist,
"The mood that had taken possession of him was a thing known to men and unknown to boys. He felt old and a little tired. Memories awoke in him. To his mind, his new sense of maturity set him apart, made of him a half-tragic figure. He wanted someone to understand the feeling that had taken possession of him after his mother's death."
Herein, the protagonist undergoes emotional transitions and is unable to comprehend with himself. therefore, through such changes and that he is moving towards manhood one can conclude that the protagonist is 19 years old.