You’ll need to pump out the atmospheric pressure anyway to replace it with fuel. Nitrogen and oxygen aren’t great fusion candidates.
Then the pinch wouldn’t occur with higher pressure. For D-D normally 7 torr (9 mbar) is used. FF reached 40 torr (53 mbar) accidentially. See https://focusfusion.org/index.php/site/article/simultaneous_firing_at_last_first_pinch_above_1_mega-amp_record-high_p/
The pressure of the fill gas is quite a parameter to tweak (one of the many variables), and there is no sound theory how to calculate it. An empirical simulation is available though, the so called Lee Model: http://www.plasmafocus.net/
