What is the time period of this story and what evidence shows it?
The story is set in the 1930s, during the Great Depression. The depression is mentioned several times. For instance, the older Scout telling the story records that
No economic fluctuations changed their status—people like the Ewells lived as guests of the county in prosperity as well as in the depths of a depression.
Further, Mrs. Merriweather notes that the only reason she keeps on her black servant Sophy is that
this depression’s on and she needs her dollar and a quarter every week she can get it.
There's also mention of Mrs. Roosevelt losing her mind for supporting African Americans. Franklin Delano Roosevelt was president during the Great Depression and Mrs. Roosevelt was the First Lady know for her courage in supporting civil rights.
Even without specific mentions of the Depression and Mrs. Roosevelt, many of the details Lee provides help establish the time period. For example, people have cars but no one is prospering, which would point to the 1930s. Children still come to school barefoot and without lunches—there is no free lunch program or anything that would indicate the more robust social welfare state of the post-World War II era.
To Kill a Mockingbird takes place in the 1930s. There are several references to the Great Depression in the story. The Great Depression began in 1929 and lasted throughout the 1930s. Atticus tells Jem and Scout why so many people in Maycomb are poor, including them:
Atticus said professional people were poor because the farmers were poor. As Maycomb County was farm country, nickels and dimes were hard to come by for doctors and dentists and lawyers (To Kill a Mockingbird, Chapter 2).
Atticus also tells his children that "the Cunninghams are country folks, farmers, and the crash hit them hardest." Everyone in town is suffering from the Depression, from the poor farmers to the educated professionals.
The WPA is also mentioned in the story. The WPA was the Works Progress Administration. It was a nationwide program created by President Franklin D. Roosevelt to provide jobs for the unemployed. Those employed by the WPA did work ranging from building roads and bridges to creating art and writing. Bob Ewell is the only person Scout knows of "who was fired from the WPA for laziness" (Chapter 27).