Minecraft wiki entry for Island_survival, associated text: Build a furnace, several stone pickaxes, and a couple of stone swords as soon as possible. Your wooden pickaxe lets you mine cobblestone, which should be easy to find by digging down a few layers into your island. Cobblestone lets you build stone tools.
Craft more torches. If you have not found any coal while digging for cobblestone, use planks (in Java Edition) or wood slabs (in Bedrock Edition), as fuel for your furnace to smelt logs to create charcoal, which you combine with sticks to make torches. You may have to wait for daytime to harvest and plant more trees to get more wood for tools and fuel.