While the idea of deep sea mining has only started to see significant effort in recent times, there were earlier efforts in the 1960s and 1970s. While they were first discovered in 1868, first recovered in 1873 and throughout the 1870s/1880s were found to occur in most oceans.
By that point there was already significant demand for many of the resources contained within manganese nodules. So there was already market for these resource. While in real life they only put effort into determining if they could be used as a source of resources in 1957/1958. But if there was significant interest they probably could have tried to figure it out earlier.
So if the mining industry became significantly interested in this source of resources around the time they were discovered, and this research was done earlier in the mid to late 1870s, how soon after could manganese nodules have been economically recovered and refined?
The resources committed to the extraction of deep sea manganese nodules would only be comparable to the potential gain, so an extraordinary amount of effort wouldn't be allocated, but there is backing by existing large mining companies so funding isn't too much of a limitation. Assume there aren't any large market shocks that would kill off projects.