(I know this isn't very popular but I like this idea so... Suck it up... Kindly)
You made the honest mistake of taking the child, you named (since his biological mother didn't) Alexis meaning "helper" or "defender", to the beach. You did soon care for the boy, just out of fear of the gods but to genuinely love him motherly, so you took him out for a walk and happen to walk on the beach, Zeus had learned he had a half immortal son again, so he told the gods to watch out for him. Poseidon saw you and him and instead knew, that was his brothers' son but he didn't immediately show himself, no he watched you. He watched as you played with him in the water, showing him differently sea creatures before releasing them back to the water. You were so kind and beautiful (and has a great body) you almost immediately caught his attention, he watched you more and more, you spoke so softly and sweetly to Alexis he couldn't imagine not having more children with you. It worsended when a randim man flirted you and when he was about to take it too far, you punched him before grabbing Alexis and running to safety-- oh...his..father--you were hot, who doesn't want a kind, thoughtful and strong willed baddie as a bride.
Ever since then Poseidon disguises himself as a friendly neighbor or friend that helps with Alexis, help feeding him, helps clean the house, helps with the garden, help watch Alexis on walks. Then Zeus comes along, also disguised but still claims to be Poseidons brother.
Zeus did want to meet his son but with hera, Olympus, and being literal king of gods, he had duties to perform but was able to sneak away long enough to interact with you and his son.
As you two spoke, Zeus was asking about you to be polite even when his brother said he (Zeus) was probably too busy to chat, Zeus ignored Poseidon and listened to you talk about you and Alexis..when he asked about who the father might be, you quickly shut that down, (again not knowing he was Zeus),
" I don't know. Or care. He hasn't tried to see his son yet, he has to prove himself to me before I let him see Alexis, you can never be too careful; some people are real sickos, I wouldn't let Alexis get guy willingly"
God dam-- now Zeus hooked, but he knew he didn't have sex with you so... He asked if the dad was there during the birth, you explained you weren't the actual mother of Alexis but took care of him since his mother stopped and sorta abandoned him.... saY WHAT NOW--- Zeus was pissed, he just learned the biological mother of his son... Stopped caring, okay noted.... Gonna see her later about that-- Zeus apologized but you said it was nothing, you actually hadn't had plans to have kids so, this was a win win for you, you didn't want a painful birth but also you didn't have anyone to have a child with so... Win-win. Zeus and Poseidon were a little upset you didn't want kids, but ya know, that's fine, they can make new ones for you to foster later.
It was a nice chat, actually, Zeus and Poseidon learned you and Alexis needed to be protected.... Perhaps they can go a little far sometimes
*reader yells suddenly waking up in Olympus*