>doesn’t require the specialized knowledge to make the alloy

Actually, iron smelting is WAY more complex than bronze smelting.

First off, ancient iron smelters were never really able to fully melt the iron (on any reliable basis) due to the limited temperatures of their furnaces. Copper and tin smelting was pretty straight forward in comparison and had lower temperature requirements to reduce and melt. Melt them together, and you got a strong useable alloy that also convenient melted at a temperature lower than just copper.

With iron, the kind of smelting they had to do was solid-state reduction of the ore - instead of smelting the ore and getting refined molten iron, they broke down and burned off/melted away the non-iron content of the ore to get a somewhat refined chunk or bloom of iron embedded with slag/charcoal. This bloom then had to be painstakingly worked - hammered and folded repeatedly while being periodically heated to a bright yellow/white glow - to consolidate the iron bloom and beat out impurities before getting a usable ingot of iron for making tools/weapons. All this needed an enormous amount of fuel, labour, and skill to perform.

Second issue. Unlike copper or tin, iron had a tendency to absorb a lot of the carbon from the burning charcoal fuel (carburization). This complicates the smelting process as iron that absorbs too much carbon turns into pig iron - A brittle ferrous alloy that couldn't be forged and had a tendency to melt and mix in with the slag during smelting. While people will later develop means to refine this pig iron into useable iron, pig iron was useless and considered an unwanted waste product by early ironworkers. As the first iron smelters figured out, you could reduce the amount of pig iron produced by maintaining a balanced airflow and temperature in the furnace, and also adding fluxing material to the smelt.

Hence, ancient iron smelters had to get a bunch of actions and conditions right in order to make good iron; without any modern measurement tools or direct knowledge of how chemical reactions and the like worked. Instead, they had to figure it all out by trial-and-error. Run the furnace too hot: excessive pig iron is produced as iron absorbs more carbon at high temperatures. Run the furnace too cold: ore doesn't get reduced. Too little airflow: fuel doesn't burn completely, furnace runs cold. Too much airflow: Iron gets re-oxidized by excess oxygen. Adding crushed limestone to the smelt: Oh, more iron!

Smelters had to maintain a constant sweet spot of furnace conditions to get it to produce iron instead of waste slag/pig iron. All this took considerable practical knowledge and experience. So it's not a surprise why it took so long to figure out how to make and use iron compare to copper or tin.

>And so weaker weapons and armor against the sea people who had iron

The thing is, there's no evidence that the Sea People had ironworking technology, at least not in the beginning. Instead, ironworking was restricted to the immediate areas under the control of the Hittites - who seemed to have kept the technology a secret and maintained a monopoly on iron production/trade. It is only after the Bronze Age collapse that we see ironworking proliferate; likely aided by former-Hittite iron smelters who were fleeing their homeland as refugees, or enslaved/assimilated by invaders. The first archeological evidence of iron smelting furnaces being operated outside the Hittite heartland of Anatolia have been dated to around 900-1000 BCE, and by 800 BCE we're seeing an enormous amount of iron being produced and used compare to what was presented during the supposed Hittite iron monopoly.