True and this was the catholic Church, yet it did have its bishops (Apostles) and it was without the written New Testament, hence the church existed before the NT canon
Churches were originally in homes, not buildings. -- homes are buildings
the first churches were in synagogues -- as you point out early Christians started off as a Jewish body, yet as they were then persecuted as supposed cannibals etc., they moved to other buildings
Church i.e. ekklesia meant/means the community.
The idea that there were home churches with each father leading the place and deciding what to do is not what Christians did -- rather, read the Didache: Christians met and celebrated the Divine Liturgy in a specific way. It may have met in homes but that was not led by someone out of the blue but by someone taught by the Apostles or by an Apostle himself.
the idea of a "home church" where someone suddenly picks up a Bible and preaches is not what happened among Early Christians who followed the teachings of Christ handed down through the Apostles -- in fact the only ones to not do so were those who twisted the words of scriptures as we see in Nicolaism and Elymas Bar-Jesus.
The early church met in homes, not buildings that were used for churches.
The first Jewish Christians went to synagogues,while Jewish customs were still being followed, but Gentile Christians began their own house churches.