Finding ammunition is brutal during the start of Fallout 4, especially for beginners who are not used to looking and scrounging everywhere. However, you can use melee weapons to kill easy enemies without wasting valuable ammunition. A simple pipe, knife, or sword will save you precious ammunition needed for the harder fights in Fallout 4.
Moreover, the Big Leagues perk in strength increases damage with melee weapons. Even one point in this perk early gives you a decent damage source when you have zero ammunition and are desperate. Be aware that playing in melee range is often dangerous, so plan your attack accordingly.