These bottles open a bit like the old style ring pulls on a can of drink, where there was a ring you lifted up and pulled kinda sideways, tearing the metal
You've managed to "pull the ring off" in the wrong direction meaning the plastic cap (the "ring") has come out of the center hole and can no longer do its work. You won't be able to refit the plastic cap no matter how hard you push
It is intended with a new bottle that you look around the edge of the bottle cap and find the marker in the metal that is the groove/line depicted in the red circle:
You put your thumbs either side of it and push the plastic lid up. This breaks the bit of metal next to the blue X and starts peeling the lid back, tearing the metal in the direction of the arrows stamped into the metal
What you'll have to do now is replicate this behavior using a strong but narrow metal stick like nail scissors, a fine screwdriver or the prongs of a fork. I'll recommend a fork.
With the bottle resting in an upright position on a firm surface, stick the fork horizontally into one of the holes marked by a green square, and directly underneath the small metal bridge next to the blue X.
Hold the bottle and push the handle of the fork down, lifting the tip up. You're aiming to break this small metal bridge.
You may need to work it from both sides, or even push the fork further so the tip of the prong comes out of the other green square hole and is past the rim of the bottle, then lever the fork upwards
After you break this bridge, remove the fork and reinsert it in the direction of the stamped metal arrows so that it goes into one of the green square holes and comes out of the black triangle hole til the prong tip is past the rim of the bottle
Lever the fork upwards, and it will "lift the ring pull" tearing the metal as it goes
Resist the temptation to grasp the metal at any point with your fingers; it will have sharp edges that cut easily.. if you must grasp it, wrap it in something or wear gloves
If you have a pair of needle nosed pliers the whole operation could perhaps be simplified to sticking them into one of the green square holes, grasping the metal bridge with them then rotating in the necessary direction to roll in the direction of the stamped arrows, winding the metal around the tip of the pliers as you go