On two different map seeds I have started, one being on a rented multiplayer server and the other a Steam provided default map, I have found lots of boar along the nearest coast to the Pillars where I spawned into the game. Keep your eye out for boar runes. There are runes dedicated to boars' and they are almost always surrounded by a handful of boars.

With a light weapon like a knife only equipped, it is possible to chase down a running deer, if you are still having problems try going pantless if wearing heavy metal armour. Better yet, when in an area where deer are known by you to spawn, hunt them wearing leather armour equipped with only a knife.