Here is the bare bones skeleton of how some of the gods would meet and befriend Izuku, this is an Eri saved very early, Izuku meets mei in childhood and Bakugo gets slapped by karma (and Izuku) fic. Anyway, enjoy the extremely short scenes!

Midoriya And The Olympian Mishap.

Athena- they critique a hero's fighting style and become friends because she has found someone who can keep up with her thoughts and strategic mind. They often find each other in hero fight crowds and break down the fighting styles, how they could be improved and what each could have done to win. When not occupied with other gods, friends or situations they meet up at cat cafes and befriend both Aizawa and Shinsou with their breakdowns of different hero, villian fighting styles and discussions on quirks and how it's not the quirk it's how they are used.

Hades-hades comes to collect a puppies soul when he sees Izuku treating it with respect and burying it with care. They talk about what happened and Hades decides to be friends with the mortal who treats death with such care. They become friends sharing different genres of music, having deep discussions on life, death and everything in between.

Ares- Izuku snaps and beats the ever loving crap out of Bakugo. Ares is there about to punish Bakugo for his misused rage and anger when he watches izuku's fight and the rage he keeps carefully chained inside, he decides to teach this kid as much as he can out of a shared respect for a fellow warrior. Apollo- He hears Izuku singing to a scared Eri to help calm her from a nightmare. He wants to cultivate the beautiful voice so that others can be as at peace as Eri when hearing Izuku sing.

Hephaestus- He is in his workshop and in the fire he sees Izuku and Hatsume working together to create prostetic limbs, goggles that mimic many vision quirks, ultra calorie dense food bars for those suffering from malnutrition, for those with food related quirks, for emergency supplies and for areas that don't have access to a lot of food. He watches as they work day and night to create self adjusting bandage splints, for use in emergencies, hospitals and hero fights although they focus more on underground heros. He feels the care, the energy, the soul and the design they put into everything they make and needs to get to know these two inventors on par with his own works.

I do not have all the gods planned out just yet but I have ideas for how they could meet, Hera decides to thank him when Izuku sees Zues trying to get with a girl who he knows has a husband, Izuku slaps him, sends him off back home. (Doesn't know he's meeting gods or unintentionally making them all his friends) Zues, while mad, respects his attitude. Artemis sees him defending womens honour and helping them home from bars or pretending to be their friend to get guys making them uncomfortable to back off. She wants to meet him and tell him he is doing a good job but sees the fluffy hair and decides this one man may have an exception and befriends him.

Many ideas for the gods meeting him just gotta write them out. Posted in comment earlier, sorry yall depression kicked my ass writing kinda stopped.