It is very possible.
Ideally you would first look for material which is in a useful state as it is. Steel would be a high priority for making tools etc and while steel can corrode quickly in the wrong conditions it is entirely plausible that heavier sections in sheltered locations could still be sound after several centuries. A good target would be machine tools and plant where high quality steel parts would be well protected inside the body of the machine and also covered in oil or grease.
Indeed it is not entirely implausible that a significant number of machines may still be restorable condition. There are plenty of 100+ year old lathes and milling machines still in operation.
Many common and useful non-ferrous metals are very easy to recycle and can just be melted in a crucible at fairly moderate temperatures which are easy to achieve with say a charcoal furnace. This includes bronze, brass, lead aluminium and copper. This process is sufficiently obvious that it is entirely plausible that it could be done with relatively little specialist knowledge or experience.
Remelting cast iron is a bit more difficult as some care needs to be taken to maintain the proper carbon content but it can be done with pretty simple equipment if you understand the process.
There is a fair chance that the amount of metal currently in circulation would keep a severely depleted population going for a long time without needing to start smelting ferrous metals from ore (or severely corroded stock)
Global annual steel production is in the order of hundreds of millions of tons so there is a lot of it about so you only need a small proportion to be accessible and in reasonably good condition to have very large stocks available and without large scale industrial projects and facilities there is a limit to the amount you are going to be able to use. Indeed before you even need to start recycling there will be plenty just stacked up in warehouses and rail yards.
A relatively simple forge using a medieval level of technology could effectively recycle most metals, although remelting steel is a bit beyond this setup it is entirely possible to forge weld assorted bits of scrap into usable billets without needing to melt it.