2023:
How do we know this event takes place in 2023?
Because in the second year of Terry McGinnis's reign as Batman he meets the infiltration unit Zeta:
Batman Beyond episode "Zeta": "Zeta was on a long term assignment, infiltrating a terrorist group; six days ago it went renegade." - Agent Bennet to Police Commissioner Barbara Gordon.
Zeta later had his own series:
The Zeta Project episode "Quality Time": "NSA File Review. Subject: Renegade Infiltration Unit Zeta. Unit Zeta went renegade August 5th, 2041, during the infiltration of suspected terrorist group Brother's Day."
Six Days after August 5, 2041 is August 11, 2041. This information is what grounded Batman Beyond in the 2040's. 2041 (Year 2 of Batman Beyond) minus 1 = 2040 (Year 1 of Batman Beyond).
JLU episode "Epilogue": "I was sixteen years old when you started training me Bruce." - Terry McGinnis in an imagined conversation with Bruce Wayne from "Epilogue".
2040 minus 16 = 2024 (the year Terry was born).
JLU episode "Epilogue": "Then I found a young Neo-Gotham couple with psychological profiles nearly identical to those of Bruce's parents. Your father thought he was getting a flu shot. Actually it was a nanotech solution programmed to rewrite his reproductive material into an exact copy of Bruce Wayne's. A little over a year later, your mother gave birth to you; a child sharing half her genetic material and half Bruce's." - Amada Waller speaking to Terry McGinnis.
2024 minus 1 = 2023.