The Order of Mata Nui predates Mata Nui himself and was formed before any Toa Teams existed, as Lesovikk’s team was the first known Toa team, and came after the Toa Mata, as well as before any Toa besides Helryx. Two former Hand of Artakha members were known to be members of the Order of Mata Nui at this time; Helryx and Hydraxon.
As I interpret the BEU’s entry, the Order of Mata Nui was formed after the Hand of Artakha, which was disbanded after 200 years of serive due to the existence of the more efficient Toa Teams. This would date the Matoran Universe to 200 years before the Shattering.
The length of the Core War is unknown. It may have been 6 months, or it could have been years, but we don’t know.
Angonance says everything changed 101,000 years ago. This might be an error, and the additional 1,000 years may be intended to be the Dark Time, however from what we’ve interpreted from the story, the Shattering happened 100,000 or 100,001 years ago. In the event that this isn’t an error, perhaps the Core War did start roughly a thousand years prior to the Shattering?
Now, there are some contridictary elements here, depending on how you configure the timeline. Going by the summary, the Hand of Artakha disbanded prior to the existence of Toa Teams, and paradoxically, due to the existence of Toa Teams. This would also require the Core War to have been at least 200 years long.
A potential solution would be that the Order of Mata Nui was formed prior to the Hand of Artakha disbanding, and instead the Hand of Artakha was active 200 years into the Matoran Universe history, after the Shattering. It’s members would then have been drafted into the Order once it disbanded, while some like Hydraxon and Helryx left prior.
So, I guess there’s two main questions at play here;
How long did the Core War, and subsequently, the construction of the Great Spirit Robot last?
Was the Order of Mata Nui formed after the Hand of Artakha disbanded, or while they were still active?