S-III Beta Company's Training

I’ve wanted to ask this question for a while as I’ve gotten a bit confused by it over the years, but when exactly did the SPARTAN-III Program’s Beta Company begin training? Was it 2537 or 2539?

Putting this under SPOILER for those who haven’t read Ghosts of Onyx and don’t want details spoiled:
Authorisation and funding for Beta were both given in the wake of Alpha Company’s destruction in late July 2537, with Kurt himself saying that 375 candidates had already been identified by that time, making one think that Beta’s candidates would have been conscripted by the end of the year, especially given the fact that Admiral Parangosky herself told Kurt and Mendez to focus on and accelerate their training. Later sources however (though I’m not entirely sure which ones) have apparently said that candidates weren’t conscripted until 2539. Is this true, and if so, why the two year wait?

It seems weird considering the timelines of the other companies. Colonel Ackerson’s proposal for the S-III Program is approved on 24 October 2531. Alpha Company begins training just two months later on 27 December 2531. Beta Company is authorised and funded immediately after Alpha’s destruction on 30 July 2537, but is postponed for two years for whatever reason despite the already identified candidates. Gamma Company apparently begins training not long after Beta’s destruction in Operation: TORPEDO on 3 July 2545, and the candidates for the proposed Delta Company were awaiting transport to Onyx just a few weeks after Gamma’s deployment when the Onyx Conflict erupted and their training was permanently postponed. Am I missing something?