Your Stone Axe can handle your first fights as well as chopping trees. Against early Greylings, favour a Torch so you can burn them with its attacks.
Once your Workbench is usable, craft a Flint Spear with 5 Wood, 10 Flint, and 2 Leather Scraps. Find Flint along shorelines and riverbanks, and hunt boars with your axe to collect the Leather Scraps.
The spear is useful for hunting deer and boars. Its secondary attack throws the weapon, which you can retrieve afterwards, giving you a ranged option without crafting arrows. Aim somewhere you can recover the spear if you miss.
Keep your first outings close to home and gather during daylight. Gradually extend your trips as you become familiar with the area.
Practise blocking, dodging, and secondary attacks against manageable enemies. Leave enough Stamina to defend yourself, recover between attacks, and give yourself room to retreat if several enemies arrive.
Before each trip, check your food, equipment condition, and remaining Rested duration. Return to rest when the buff runs low, and head home before your supplies run out.