Below is an old post of mine, from before Halo 5 released and from before Hwars 2 was announced - therefore, ignore the Red Team theories. However, I’m sharing it because it compiles relevant information about Spartan-II possibilities. 
The real discrepancies, then, perhaps lie in the Spartan-II deployments to Reach during the invasion. Red Team, according to the 2010 First Strike reprint, consisted of 22 Spartan-II commandos deployed to the surface. So let’s look at our 33 Spartans, and see who could have been on this team?
Spartan - State of Service - CAPABLE of being present in Reach’s Red Team (2552)?
James-005 - Deployed with S-117 above Reach - No
Jai-006 - Gray Team - No
Li-008 - Red Team - Yes
Naomi-010 - Red Team - Yes
Daisy-023 - KIA 2531 - No
Joshua-029 - Red Team - Yes
Vinh-030 - Red Team - Yes
Sam-034 - KIA 2525 - No
Randall-037 - MIA 2537, Discharged 2546 - No
Isaac-039 - Red Team - Yes
Douglas-042 - MIA 2531 - No
William-043 - Red Team - Yes
Anton-044 - Red Team - Yes
Keiichi-047 - Possible Red Team - Yes
Kurt-051 - Training Spartan-III - No
Jorge-052 - Noble Team - No
Linda-058 - Deployed with S-117 above Reach - No
Malcolm-059 - Red Team - Yes
Maria-062 - Retired, UNSC reserves on Earth - No
Sheila-065 - KIA 2544 - No
Solomon-069 - KIA 2544 - No
Arthur-079 - KIA 2544 - No
Kelly-087 - Red Team - Yes
Jerome-092 - MIA 2531 - No
Grace-093 - Red Team - Yes
Fred-104 - Red Team Leader - Yes
Adriana-111 - Gray Team - No
John-117 - Deployed above Reach - No
Mike-120 - Gray Team - No
Joseph-122 - Escaped Trainee Post-Augmentation, Possibly continued training (Suicide NEVER confirmed) - Yes
Oscar-129 - KIA 2525 (suicide) - No
Alice-130 - MIA 2531 - No
Cal-141 - KIA between 2540-2551 - No
From this list of active-duty Spartan-IIs who successfully graduated the program, we see thirteen possible Spartans of the twenty-two said to be deployed on Reach’s surface in Red Team. There are some variables we could play with here:
-Presume Spartan-Red from the Spirit of Fire actually made it back to UNSC-controlled space prior to 2552 [Add three]
** The SoF crew has no lore pertaining to them following 2531, save for that the ship was seen, seemingly abandoned, with a flood spore. While extremely unlikely, you could technically add them back into the mix.
-Kirk-018 and Rene-081 were hoped by Halsey to be rehabilitated and possibly re-instated at some point prior to 2552. [Add two]
-Additionally to the above, only eight of twelve failed augmentations have been named and reported on. It is possible that, like Kirk-018 and Rene-081, these remaining four might have eventually been rehabilitated and re-instated into the Spartan-II program. [Add four].
13 + 3 + 2 + 4 = 22.
Therefore, if we make some bold assumptions, then and only then could the First Strike Red Team deployment make sense. Otherwise, that remains a discrepancy for which we’ll have to await a remedy. One other permutation of this 22-number could involve, again, more rehabilitated Spartan-IIs: subtract Spirit of Fire’s Red Team (as their presence is extremely unlikely), add in three Spartan-IIs who were technically KIA during augmentations, later revived as technologies improved, and re-entered service. I don’t like this approach either, because we have a massive pool of 25-unnamed KIA Spartan-IIs to pull from and it seems cheap, ineffective storytelling.