I was going to hold off on saying anything but I can't control myself. The Oldest Watch Contest hasn't been held in several years. The management that influenced that contest has retired or left Longines for other careers. Not sure if there will be any future Oldest Watch Contest in the near future 183 may have made that contest pointless.
Also, watches in the past, I believe all had Longines original cases, movements, dial, and hands. So high original content was needed to be selected. The watch that won the UK for example, Longines actually even replaced the bow with an original one to make it more original.
Your watch has a case that does not appear to be Longines made. The stamped numbers match your serial number, however, they are not Longines factory numbers and not stamped in the fashion normally done by the factory as far as I know. I also do not see an EF Longines Co logo on your case. The case for the watch maybe locally produced in the country it was delivered to.
I would not throw the watch away, but if you are looking for a ultra low serial number, you might want to continue looking for something under 1,000; which are pretty darn hard to find as many are now in collections.
Your watch has a case that does not appear to be Longines made. The stamped numbers match your serial number, however, they are not Longines factory numbers and not stamped in the fashion normally done by the factory as far as I know. I also do not see an EF Longines Co logo on your case. The case for the watch maybe locally produced in the country it was delivered to.
My impression is that Longines was not making its own cases prior to 1880 (source: chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.watkinsr.id.au/Francillon.pdf). In my view, the numbers on this case are stamped in a manner that is typical of other Longines from the period. I would not expect to see an "EF Longines Co" logo on the case. See some examples below.
I haven't looked at 20B as I think there are hundreds of them up for sale and too many possibilities. You might be right that no EF Longines Co. logo was used during the period of the posters watch. I would perfer a watch that at least had Longines written on the cuvette otherwise the case could have come from anywhere.
I do not think that the absence of "Longines" on the cuvette is of particular significance with respect to where a case came from. Many original Swiss cases do not have such a marking. Maybe more important are other markings that are typical such as apparent maker's marks and numbers.
I'm currently trying to locate a bezel for the case and a period correct crystal if possible
I think that finding another watch with those parts might be the simplest option. I notice that there is also a component missing that mates with a key for setting the time (highlighted below).