Yes. Thank you for this. I've heard in my own Church that it began with His incarnation, while others say it began with the harrowing of Hell (cf. entering the strongman's house and taking his goods as a metaphor for the freeing of those who were captive in Hades), so what I'm really wondering about by this question is the range of thought about this in the EO Church.
I'm not sure if many of the Fathers made definitive statements as to when as an exact starting point. Usually we generically say the millenial reign started with the first coming and ends with the second, and even then, it ends just prior to that. When the gospel is preached to the ends of the earth followed by the removal of the restraining force.
Jesus cried out on the cross, "It is finished", so in my opinion there is leeway as to which event(s) ushered all this in.
If that’s the case though how do you explain all the evil in the world?
When Christ said to his disciples he saw Satan cast down from heaven, it was tied to the 70 preaching the gospel and their ability to cast out the demons. He tells them if a city does not welcome them to leave but to always remember the kingdom of God has come upon the world. It does not signify a peaceful utopia just the ability to cast them out and plunder their goods (harvest souls) (Luke 10:17-20).
Then we have the parable of entering the strong man's house and binding him and plundering his house. This gives us the sense as to what is meant by binding Satan and plundering his house:
But when the Pharisees heard this, they said, “It is only by Beelzebul, the prince of demons, that this fellow drives out demons.”
25 Jesus knew their thoughts and said to them, “Every kingdom divided against itself will be ruined, and every city or household divided against itself will not stand. 26 If Satan drives out Satan, he is divided against himself. How then can his kingdom stand? 27 And if I drive out demons by Beelzebul, by whom do your people drive them out? So then, they will be your judges. 28 But if it is by the Spirit of God that I drive out demons, then the kingdom of God has come upon you. Or else how can one enter into a strong man's house, and spoil his goods, except he first bind the strong man? and then he will spoil his house. Matt 12