Is there any way I can open it?
A couple of possibilities here:
Dev Tools is disabled, either because you're not on a real page (for instance, the default home page when you first open it), or because your organization's Active Directory configuration doesn't allow it.
Something else must be consuming the F12 (for instance, if you're running a virtual machine, perhaps the virtual machine software is using F12 as the "host" key).
If Dev Tools isn't disabled, you can always open Dev Tools from the gear menu: