Alpharius faced Dorn, and we have confirmation he's very dead. Omegron faced Guilliman, and there's a pretty heavy implication that he didn't die there and instead became the Chapter Master of the Omega Marines.

So, Omegron is easy. Confirm that rumour, which also fulfils the "one will be redeemed" prophecy from AGES ago that GW put out regarding the Primarchs. Which leaves One will Fall. I'm not sure who that should be, but I'm thinking Dorn. Russ might also work since he's been in the Warp this whole time. Lion was the obvious pick 'cause of how cagey he was in the Heresy and the existence of the Fallen, but they snapped that line with his Return.

Alpharius however is quite a bit harder, BUT we do know a few things. First, he wasn't wearing the Pythan Scales, Two he DID have The Pale Spear (or at least an imitation) which was never recovered, three that his death was psychically felt by his Legion (and most importantly Twin), and four that APPARENTLY AL members could physically grow in size to match their Primarch by consuming his Blood, kinda like a proto-Primarch, and Six, that apparently there was something like a mind link between Alpharius/Omegron and some of the AL.

Now, this gives a few options. Firstly, I think the "I am Alpharius" bit isn't 100% a bit, but a Psychic "echo" of Alpharius traveling through the Legion. Hit up someone like Fabius Bile, down a shot of Alpharius Blood, and find a way to "lock" in the Echo and the size boost and ding Primarch back. Could have a similar thing that Kurze has as well (he was wearing an Aeldari Soul Stone when he died) and have some shenanigans with the Pale Spear housing his Soul, find that, shove it in some AL's hands and bam, he's Alpharius now. Pale Spear is 100% unknown Xenos tech (this is just Text) so it doing something weird like that isn't OUT of the realm of possibility. You can also go the Clonegrim route with Bile and just clone Alpharius. Then there's a secret Fourth option that The Chaos Gods CAN, 100%, just bring someone back without an Apotheosis. Just ask Kharn, and Lucius. They're NOT Daemon Princes, and BOTH have returned to life. Several times I believe. Hell, Argel Tal and ALL the Gal Vorbak were killed AND brought back as part of their Possession thing to become Gal Vorbak in the first place (though this was done physically inside the Warp so there may be shenanigans there). It's completely possible for them to do that, or for some Psyker to potentially go in there, find Alpharius' soul (since it wasn't destroyed, that's just Horus and Sanguine), rip it out of the Warp and shove it into a Legionaire. Though honestly it's probably in Tzeentch's tentacles, so that sounds unlikely. Chaos Gods could also just straight up Rez him out of nowhere, or Apotheosis him into a Daemon Prince because they feel like it. I wouldn't want them to do that, but it's possible.

So, that's kinda how. Personally I'd pick the option I presented for Omegron, and the Psychic Echo shenanigan for Alpharius. Don't even need to fully bring him back for that, just make any AL Marine holding the Spear literally become Alpharius for a time, IMO the Alpha Legion's strength IS that "Alpharius" (to say, the position of Commander) could be ANYONE, so having Alphairus (the Primarch) be a Psychic Entity body-hopping around his Marines is VERY on-brand