If playing in a Survival world in Minecraft, you essentially already have an infinite supply of Cobblestone blocks to access. All you need to do is dig underneath you to find Stone blocks that you can break down into Cobblestone, and you are set. However, if you are playing in a situation where there are not many resources for you, like a Skyblock server, you may need to think of some unique ways to acquire Cobblestone for access to a Stone Pickaxe. Here is how to make a Cobblestone generator in Minecraft.
Making Cobblestone in Minecraft is incredibly easy and will only require creating a hole and filling two buckets, one with lava and one with water. When you have your buckets, find the location you want to create the Cobblestone in and punch out a line of four blocks. Now in one of the inner blocks that you have dug out, dig one block down.
Whatever side you have dug that extra hole down into, place your water on the end. It will flow down into the hole. Now on the opposite side, place your lava. The lava will flow into the falling water and create Cobblestone. Note that if you swap the lava and water placement, your water will go into the lava source block and create Obsidian instead of Cobblestone, ending in needing another bucket of lava.
Once your Cobblestone has been created, all you need to do is simply grab a pickaxe, break down the Cobblestone, and another will immediately replace it. This will give you an infinite supply of Cobblestone without needing to leave and go underground.