I think he's an alpha. It doesn't make sense otherwise. Firstly, he doesn't have the standard look of an omega. Till now we didn't see a buff omega. Secondly, in Hye-sung's memories he showed "distinct alpha traits". He was aggressive, dominant and imposing. And lastly, if he was an omega, that would make the mother an alpha, which doesn't make sense. Why would she, an alpha, find another alpha? And how would he even get an upper hand to abuse her?
So I think the "I gave birth to him" might be a slight mistranslation, or simply meaning "he also made him, thus helping him being born"...
wait a minute somebody help me understand this. So Hyesung’s dad is an omega?? I’m a tad lost at this sudden twist in the plot