While I play single player and go into any menu (esc, inventory, etc) it pauses my game. How can I go into menu without pausing the game?
The only way the you can sort through your inventory without everything freezing up is by playing multiplayer.
If you play it as single-player, you'll have to keep pausing the game every time you open the menu.
So my advice? Open up your lobby; set your connection type to "Public". That'll allow others in Matchmaking to find and join you, then allowing you to take advantage of that to not have menus pause the games.