EAC Error '3005' createfile failed in sys32

I opened an html file starting with "BF2042_" in this folder (ProgramData is a hidden folder so you'd need to make sure hidden files and folders are visible if you're clicking through):

C:\ProgramData\Origin\Logs\

and found errors (highlighted in red) saying:

"Failure opening file to save license. Path: C:\ProgramData\Electronic Arts\EA Services\License\193874.dlf"

So I went to this folder

C:\ProgramData\Electronic Arts\EA Services\

Then, right click the License directory

Select Properties > Security > Edit...

Scroll down the list under "Group or user names" to find "Users (YourPCName\Users)",

Select that and tick Allow for Full Control.

And the game finally launched for me.

Might not be exactly the same issue for you but you could check one of those log files and see if an error points you to a folder that needs its permissions changed.