I think your question is "when were the antidepressants that are often prescribed today first prescribed?" Correct me if I'm wrong.

The modern era of psychopharmacology really begins in the 1950s, when certain mood changes noted as side effects of some tuberculosis drugs were explored. This led to the first MAO inhibitors (rarely but occasionally still used these days). Further research led to the development of tricyclic antidepressants. Some of these are still in common use today. Amitriptyline was developed in 1961 and is still widely prescribed, but almost exclusively for its effects on nerve pain rather than its antidepressant properties. Fluoxetine (Prozac) was the first well-known SSRI drug and wasn't developed until the 1980s.

A rather dense and nerdy summary of the development of antidepressant medications

A less focused but much more readable article on both the history of antidepressant drugs and how these medications have influenced concepts of the physiology of depression