Indiana Jones and the Great Circle's disguises just help the game go down smoother, freeing you from dealing with its tedious stealth and letting you focus on exploration and puzzle solving. Prioritizing getting the best disguises as quickly as possible is 100% the move to best enjoy this game.
In the game's first zone, the Vatican, the outfit that will let you access restricted areas is the Blackshirt disguise, which can be unlocked only after progressing the main quest far enough. It is also easier to find on your map if you begin the Underground Boxing Ring sidequest, which will give you a quest marker for the disguise.
