The situation of Final Approach involves an experimental government operation ("R.T.P.") to oppose the declining birthrates of Japan, circa this period in time. The primary decision was to arrange a national project in which young citizens of opposite sexes are to be paired together in marriage, and therefore in parenthood.
While the economical and political gains are great, the social and emotional aspects of the "subjects" in the project are easily assumed adamant in defending the previous method of marriage. Thus, the Japanese government decided to test the project on an experimental level, i.e. with one couple at a time.
The Mizuhara siblings are the first to be chosen for the R.T.P. project. The brother and the sister, Ryo and Akane, have long been living together in the same apartment. Still in public school, the two have endured a difficult life after their parents' death some years back. Ryo, the main protagonist, has assured to himself that all is well; he and his sister are living on well-paid wages, and he only needs his sister. The vision of his future is soon to be shattered by the R.T.P. when his planned fiancée, Shizuka, enters his apartment one night with several government bodyguards. By some preliminary actions taken by the government (as precautions), Ryo is forced to house his new wife-to-be, despite his refusal.