In the beginning of Scene I, Tom as narrator introduces the characters along with himself. Pointing to the mantel where a "larger-than-life-size photograph" hangs, Tom refers to the fifth character, his father, who was a telephone man. Tom describes him as a man who "fell in love with long distances," leaving his job and his home. All he did was send a postcard from Mazatlan on the coast of Mexico that read "Hello--Good-bye!" with no return address.
This photograph of Mr. Wingfield shows a young man in a World War I cap. Since the play is set in 1944, the time of the second world war, the father has obviously been gone for a long time, and was probably rather young when he left. However, no mention of the year that he left is made. Since The Glass Menagerie has elements of autobiography in it, and Tennessee Williams's father left his family when Williams was only seven, this age may be the approximate one for Tom, as well.
Later, in Scene II when Amanda returns home after discovering that Laura has not been attending Rubicam's Business College, she bemoans the fact that they will have nothing for the rest of their lives:
"What is there left but dependency all our lives?"
This reflection suggests that the Wingfields have been dependent for some time, and Amanda worries that this will continue. Further in this same scene Amanda comes out wearing "a very old bathrobe...a relic of the faithless Mr. Wingfield," so, again, there is the suggestion that the father has been absent for a very long time.