A note - This is very much designed with the amazing HUD Toggle mod in mind from TheJanitor - https://www.nexusmods.com/daysgone/mods/8 

I changed my .ini settings for that mod to these for gamepad use so that the HUD comes up only when aiming or holding down left trigger. I set the toggle key to holding the down button on the d-pad with a slight delay so that I wont turn on the flashlight by mistake (tap to turn on flashlight, hold to toggle HUD. Clicking-and-holding the right thumbstick will show the HUD and holding the X button (reload button) will bring up the HUD as well. This works especially well for opening car hoods and trunks. Holding Left bumper will bring up the HUD so you can do crafting and weapon switching with ease. Clicking-and-holding the left thumbstick will bring up HUD as well:

[Key2]      
Key = XB_DPAD_DOWN
x = 0
type = toggle
Delay = 200

; Hold to show weapon wheel for Xbox controller:

[Key3]      
Key = XB_LEFT_TRIGGER
x = 1
type = hold
Delay = 1

[Key5]      
Key = XB_LEFT_THUMB
x = 1
type = hold
Delay = 1

[Key7]      
Key = XB_RIGHT_THUMB
x = 1
type = hold
Delay = 1

[Key8]      
Key = XB_LEFT_SHOULDER
x = 1
type = hold
Delay = 1

[Key6]      
Key = XB_X
x = 1
type = hold
Delay = 100

I'm sure all of these settings could be set in a similar manner for keyboard and mouse, I simply don't play with K&M so can't suggest settings. But you can just change the hotkey for whatever you use that corresponds to the most convenient controls for you. The idea is just to set as many keys as hotkeys to bring up the HUD on the "hold" type that are used in game as possible, so that you can always have the HUD up when you need it and let it automatically stay hidden when you don't during exploration and combat, like survival mode basically.

If you don't use this mod, you may want to drastically shrink the letterbox so you can see other parts of your HUD more easily.