"simply given that" is correct and usable in written English.
It is used to indicate that something is a logical consequence of the previously mentioned facts. For example: We should not be surprised that the youngest child won the race, simply given that he is the oldest and most experienced runner.
Red lipstick worn with plaited hair, a tracksuit and trainers will simply give that all-important bright, energetic look.
He suggested that Mr. Romney had been the architect of a "government-run" health care system and "would simply give that issue away in the fall".
In empowering the Yazidi refugees, the P.K.K. had created a new base of sympathy for its revolutionary cause; they seemed unlikely to simply give that up.
Instead of simply giving that donor's kidney to the next patient in line, the kidney can go to the would-be recipient in an incompatible donor-recipient pair; that donor, in turn, can then give to another recipient of an incompatible donor-recipient pair, with the chain continuing indefinitely.
Meanwhile it simply gives that information, gives us, to the Deep State, the U.S. shadow corporate government that has formed at the crossroads of surveillance corporations and Wall Street.
For the latter, a simple question was asked; was it leadership to be the one in front with the idea, plan and passion, or was true leadership simply giving that person the room to run with it?
Simply give that Pokémon to your friend in the battle, replace it with the Pokemon evolved form, and take back your Pokémon.
Given that, simply pointing out that something is public as the sole reason for republishing it is not a sufficient justification.
For some it is a cultural practice handed down through the generations, an unquestioned given that is simply adopted.
