Lemme have a shot, though I’m not a metallurgist. You smelt simply by removing the oxygen from the iron oxide. Take magnetite sand, Fe3O4. You can remove the oxygen and produce iron/steel in a small charcoal fire with enough air blown into it (1,200 degrees centigrade.) Unfortunately, with this method, you produce inconsistent lumps from the furnace: un-smelted magnetite, iron, low- and high-carbon steel.
The above method is really a hit-and-miss process, and you have to test each lump of steel that comes out for the right carbon content. Some improvements in insulating the smelt within a clay vessel (crucible or wootz steel) were done but the result was the same. Once you have enough steel of the right carbon content, it’s up to you to do what you want with it, whether to forge each piece, or pattern-weld several pieces, or stack/layer forge them. The Japanese tataras that produce sword-quality steel are like this. They produce a non-homogenous lump that has to be broken up and the fragments sorted.
In the blooming process, you produce molten steel of the right carbon content you want and pour it into a mold to form a block or a bloom, from where you can shape it into the form you want (like sheets). Plate armor for knights was possible only with the blooming method. Before that, you had only steel rings and small greaves for armor material. How to produce a bloom? Easy, heat to past 1,600 degrees, which was beyond most charcoal hand-blown furnaces during ancient to post-medieval time. Find a way to separate the molten silicates (slag) from the un-smelted oxides and iron (matte) from the molten steel. You are looking to tap the molten steel last and mold it into your bloom.
Producing bloom steel was one major step in man’s march to industrialization.
Who smelted first? Not an expert on that.