In the ep "Divided Loyalties" Ivanova tells Sheridan that her mother taught her how to avoid the tests at school. So, I am making the assumption that regular tests for psi-ability were done on all kids from an early age - much like schools test for hearing and sight now [do they do that in the States?]. We aren't told how often they are done, but it must be at least once every couple of years or so
Obviously, it varies a great deal as to when psi-ability manifests itself. Some would be active telepaths at birth - especially if both their parents were telepaths. Some would start to show ability as they grew up. Others would manifest at puberty.
Telepathic ability does in some cases seem to manifest itself suddenly and unexpectidly - with no prior history in the family. There is the young girl in "Legacies" who is in the middle of shoplifting when her ability seems to suddenly just 'wake up'. She screams and collapses.
And there is the Psi-Corps member who acompanies that power-mad Colonel [sorry can't remember his name] in "Eyes". He tells Ivanova that at sixteen he had joined Earthforce to become a fighter pilot - and Earthforce probably has tests for psi-ability as well, when his abilities manifested at sixteen.