Forget worrying about the cooler pocket and get one of these.
https://www.amazon.com/Frostbox-Cooler-Accessories-Coolers-Discrete/dp/B08PQMLR84/ref=asc_df_B08PQMLR84/?tag=hyprod-20&linkCode=df0&hvadid=647175602871&hvpos=&hvnetw=g&hvrand=12950498762281956215&hvpone=&hvptwo=&hvqmt=&hvdev=m&hvdvcmdl=&hvlocint=&hvlocphy=1023416&hvtargid=pla-1957244870852&psc=1&gclid=Cj0KCQjwtO-kBhDIARIsAL6LoreGe5VFFvr67OGXOqzTykwxWYdJyqHpLupMzZvy_6m5VF3D0_TyBOsaAmw7EALw_wcB