Before 2020:
JLU episode "Epilogue": "I saw him save the day dozens of times with nothing but his wits, body and will. But I saw something else as the years passed: he was getting older; slower. Soon he'd have to retire or more likely someone would finally manage to kill him. The thought of a world without Batman was unacceptable. So I decided to make a new one. I used my old Cadmus connections to gather the technology necessary for Project Batman Beyond. Bruce's DNA was easy enough to obtain; he left it all over town. Then I found a young Neo-Gotham couple with psychological profiles nearly identical to those of Bruce's parents." - Amada Waller speaking to Terry McGinnis.
We know these events take place before 2020 because they take place before Batman starts wearing the 'Batman Beyond' suit (which he does at some undisclosed time before or during 2020 per "Rebirth, Part I") and before Bruce retires (which he does in 2020, also per "Rebirth, Part I"). For information on how we know when Batman Retires see the 2020 entry.