I dug myself a Heffalump trap with the way I worded the last sentence. I really should have written "There are other ways which
may produce an answer with men who survived but are not relevant to your case so I don't list them here".
There is no one size fits all system, not surprising given that the army numbering system has more minefields than the South/North Korean border. In the background is, among others, the regimental nature of the system until after the war which produces men with the same number in different regiments, the change of numbers when a man changed unit and the 1917 re-numbering of the Territorial Force.
These are places which have solid data.
http://armyservicenumbers.blogspot.com/p/index.html should be the first port of call but does not purport to cover all battalions or indeed all regiments and corps or much beyond 1914 in most cases.
The records of recipients of the Silver War Badge usually have the date of enlistment as part of the record.
The Royal Artillery Attestation records and the Tank Corps Enlistment records which includes the cavalry (it says 1919 but includes earlier dates) on FindMyPast have enlistment dates.
There are then the “look for clues” approaches.
The “near numbers” trick is where one searches for surviving records of men (including those that themselves did not survive)in the same battalion with numbers very near to the one you seek. Not foolproof but may with other clues give the answer.
The Longlongtrail has a number of info pieces on numbering and re-numbering which can give pointers.
There are reference/history books such as for example No Labour No Battle, the history of the Labour Corps which has guidance for Labour Corps numbers which can sometimes be used as a start point for further research.
There are researchers, regimental museums and some web sites where a specific study has been made of a particular unit (there is one on Sherwood Foresters). They aren’t listed anywhere, they have to be ferreted out.
Take a moment to look at this forum (and if you can, others concerned specifically with the Great War) to see the queries related to enlistment dates and note the variety of approaches in the answers, many (most?) of which don’t come up with anything definite. All indicating that except in some cases it is a matter of casting around in as many directions as possible and of adding clues together .
This is probably getting a bit incoherent now and I may have missed something obvious in which case I’m sure someone will let me know! I should make sure I emphasise the caveat that all these ideas
might give the answer.
This last is going to sound a bit OTT but one has to have a fairly broad understanding of the way the army works. Knowing where to look is only half the battle, the other half is knowing how to cross check your result before going firm on a date.
MaxD