From this page of the Hitman 3 guide, you will learn how to hack the Data Core and safely escape from the ICA facility while completing the End Of An Era mission taking place in Chongqing, China.
The ability to hack the Data Core will only appear once you have eliminated both targets. The best opportunity to complete this task comes after completing the Impulse Control mission story, as you will be able to start at the ICA facility.
In the room where Imogen Royce gave you her presentation you will find a ventilation duct. Take the screwdriver from the desk and open the ventilation grille, then go down the ladder to the lower floor.
If you want, you can of course open the ventilation shaft grilles with your camera.
Open the vent, but exit into the corridor only when the guard is not looking in your direction. Head to the right side. If the double doors on the left are closed, use the ventilation duct shown in the image above.
After entering the shaft, walk ahead, turn right, then left and left again. Continuing forward you will reach a ventilation grille - open it.
Go through the small room, open another vent and go into the room with the Data Core. Now all you have to do is use the touch terminal and follow the steps ordered by Olivia and the task will be over.
Unfortunately, your presence will be detected and you will have to flee the ICA area. Run into the ventilation duct you used to get here.
Going to the left you will reach one of the rooms of the facility. Hide behind the table and wait for a moment, then run behind the guards' backs into the opposite room.
Continue forward and you will reach a room with one guard. Behind the metal cabinets, on the right, you will find the entrance to a ventilation duct - enter it. Continue by climbing the ladder to the upper floor, and you'll be back in the room from where you started your journey to the Data Core.
Exit the room, turn left and take the stairs to the upper floor of the facility. Go into the narrow hallway.
Continuing forward you will come to a room with computers. Sneak behind the desks into the air duct.
When the guards are not looking in your direction, leave the room and take the stairs to the top floor. Open the double doors and go outside. You can now go to one of the exits available in the Chongqing area to complete the missions in China.