From a writing and storytelling perspective, I think it's both hilarious and poignant that the central question to the plot of Mamma Mia just... never gets answered. Neither the characters nor the audience ever finds out who Sophie's biological father is. No DNA tests are taken. Even in the second film, set a decade (or more) later, with better technology, it's clear it never really occurred to anyone to do a DNA test. This central question is an objective question that they could absolutely answer with semi-readily available resources.
That's honestly hilarious.
But I also understand why it's never answered: because the nature of the central question itself changed. Sophie naturally wanted her dad at her wedding, but she accomplished that by successfully inviting all three of her potential fathers to the wedding and them all showing up. But then we, the audience, are faced with the idea that Sophie knows having her father there doesn't necessarily make her family whole, but what it really represents is that if she can solve this last mystery of her childhood, she can close the door on her youth, marry Sky and therefore symbolically become an adult, and then focus on the future by taking care of her mother and her mother's legacy, AKA the hotel. Between the hotel and Donna's single motherhood, Sophie has internalized adulthood as responsibility and caring for others.
When I was young, it confused me why Sophie and Sky don't still get married at the end of the musical when it establishes them as still in love and leaving the island together. I now think it's tied to how this central question not only isn't answered but how the nature of the question changes. The Dads, unintentionally, challenge Sophie's understanding of what adulthood is. Just by asking about her interests, and telling her their stories of facing adulthood, she's forced to consider whether she's following her own dreams or whether she's following in her mother's footsteps but with the right man this time (because that's The Right Thing For The Family). It's more subtle with Sky, but as the musical goes on, it argues that Sophie and Sky might be legally adults, but they don't have adult maturity, and marrying won't make them adults - they truly love each other, yes, and they value being committed to each other, yes, but also, yes, they're too young to get married.
Sophie is a complete woman even though she grew up in a single-parent household, and you don't have to have a perfect family to become complete - but Sophie isn't a "finished" woman; she still has a lot to learn and experience and accomplish, and she could still use some guidance from her parents as she does that. That's why it's important how Sophie leaves the island at the end - it's not a scene in an airport with Donna hugging Sophie goodbye and watching Sophie walk onto a plane alone; in the scene, Sophie gets on a boat with Sky and more importantly her dads, who are committed to supporting her dreams. Sophie wanted her dad, but when she realized she ended up with not just a dad but three "a" dads, she realized it didn't really matter which was the mystery man she was searching for because they all wanted to be part of her real life. For the Dads, what matters is that she could be their kid, so she will be their kid, because whether they're blood shouldn't be an obstacle between what they want, which is to love and support this kid who is kind to them and is a product of a woman who they once loved.
The question isn't definitively answered for the audience because the characters choose their own answer.
And that's pretty poignant if you ask me.
