Ah, no you can’t add it to the inbox. You can however make your filter your replacement inbox by setting it as your default workspace. That option is right down next to the edit button.
I should note that the inability to add this to the inbox is on purpose. The goal of the inbox is in fact to make staff take the ticket. That’s because once it’s owned by someone, anyone then it’s much more likely to get worked on promptly even if that person needs to reassign it to the proper person. One of the major problems with many help desk systems is they make it easy to look at the ticket without taking it. This allows staff to easily cherry pick requests.
This may not be appropriate for your case so you can use the filter work around, but that’s the general logic.