A paella pan is the opposite of a Dutch oven. Instead of trapping steam and braising low and slow, it spreads the liquid thin so every grain of rice has a chance to toast on the bottom of the pan.
That toasted bottom layer is called socarrat, and it is the defining feature of a great paella. It is not a mistake or a burn, but a deliberate caramelization that you build in the last few minutes by turning the heat up and listening.
The hardest part about cooking paella is leaving it alone. No stirring. Once the rice is in the pan with the stock, you arrange the ingredients on top and walk away. Any stirring releases starch and you end up with risotto, which is wonderful but not what we are after.
If you do not own a paella pan, any wide, shallow, flat-bottomed skillet will do. Cast iron works beautifully. What matters is the surface area, not the material.