Technically, but not really. You have to get wood for stone and stone for iron, which you need 3 iron ingots for 1 bucket.
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You make them out of wood or smooth stone (not cobble). The wood ones can detect items and mobs/players, the smooth stone only the mobs/players. You make them like this: xxx xxx mmx where x is nothing and m is wood or smoothstone
get wood and turn them in to planks
wood->stone->steel->diamond gold is as strong as wood but as fast as diamond
If you can find a village, steal wood from them, break it into sticks, and create a wooden pickaxe. Then, once you have enough stone, make a stone pickaxe.
you can make a sword, and bow. the sword can be in wood, stone, iron, gold, or diamond. you need three of these and a stick to make. diamond is the best to make the bow you need some string and sticks.