Is this every session or just happened once?
Surprisingly I can get hits on enemy players like there's no problem because the mouse movements are fine and the hitmarkers are on time. It's the moving and the other actions that are delayed (gun switch, gadget deployment, revives,...).
Tried unplugging the superfluous USB devices and play, no difference. Origin in-game is disabled, I also deleted the file "IGO64.dll" in [C:\program files (x86)\Origin] as it was suggested in a video, no changes. Game starts fine, in the menu works fine but when I start a mach the game works fine for the first seconds the the input lag starts increasing more and more until it gets unplayable.
I tried also to repair the game and re-installing it. No results.
What keyboard and mouse are you using?