It took thousands of years for iron to overtake the use of bronze
Depends on how you look at it. From the moment ppl found out they can work the metal (to when the same ppl made it feasible and started using it for real)? Yes. Too difficult at first.
For it to spread worldwide? Again, yes, information didn't travel that fast, and many nations kinda wanted to monopolize this advantage for either trade or war.
But once it had become feasible (something mc should be able to achieve near instantly) and someone put the knowledge to practice, it was all an inevitability from there. Doesn't matter how long it took, the pioneers still unlocked everything that came after. And in terms of the direct geographical area, it probably will be as quick as a couple generations for the tech to leak (or village start trading actual weapons) and seeing proliferate use in their wars. Which will quickly have surrounding nations steal the knowledge in a similarly short timeframe, and so on it goes (even if they manage to stop that, nations don't live long in general (mere centuries at most). And once this nation collapses or has civil war, the lid will come off forcefully all at once).
In summary, I think it's not too unlikely for things to go similarly quickly in that isekai world, as it did in ours, and will likely even happen faster (so I would estimate it to be around a single millenia at the far end, and probably be widespread in their general geographical area already within the first 2-3 centuries).