Historically, when did the Ashkenazi custom to bake matza on erev Pesach afternoon start? I am specifically interested in when this custom arose, rather than the reasons/opions pro/against.
Sefer HaToda'ah (Translated in English as "The Book of Our Heritage"), says that this custom originates in the Talmud Yerushamli, and is brought by many of the early codifiers.
The reason given is that the Torah connected the Korban Pesach to the Matzah. Since the Korban Pesach must be slaughtered after midday, so too must the Matzah used at the Seder be baked after midday.
These Matzot are called "Matzot Mitzvah".
Regarding baking Matzos on Erev Pesach there are those that do it and those who do not. Those who do it - rely on Orach Chaim 458, Leket Yosher 79, Magen Avrohom, Sidur Yaavetz, Pri Megadim, Shulchan Aruch HaRav, Yalkot MaiAm Loez.
However there are those that do not bake after Chatzos due to the fact that it may become Chometz and at that time a person is not supposed to have any Chometz any more. Mishna Berura, Gra.