it's a valid question - i would say it differs depending on usage, so capitalize when you're using it in a formal or titular way ("The Alpha spoke"/"but he was the first Omega in his friend group"/"Betas had a different responsibility") and stick with lowercase for more descriptive, casual sentences ("his omega preened"/"he didn't smell like an alpha"/"a self-defense class for omegas" etc)

but rlly fiction is a wonderland and omegaverse isnt reallll so do whatever you want! have fun