This heart-meltingly romantic and sad movie from Korean-Canadian dramatist and film-maker Celine Song left me wrung out and empty and weirdly euphoric, as if I’d lived through an 18-month affair in the course of an hour and three-quarters. How extraordinary to think that this is Song’s feature debut. It’s delicate, sophisticated and yet also somehow simple, direct, even verging on the cheesy. Past Lives has been compared to the movies of Richard Linklater, Noah Baumbach and Greta Gerwig; all true, but I also found myself remembering the wrenching final moments of Wong Kar-wai’s In the Mood for Love, with Tony Leung murmuring his pain into a stone hollow in Angkor Wat and – yes – the gooey genius of Dean Friedman’s plaintive 1978 chart hit Lucky Stars.

This is a story of lost love and childhood crush, the painful and dangerous access to the past given by digital media; the roads not taken, the lives not led, the futile luxury of regret. And it’s a movie that speaks to the migrant experience and the way this creates lifelong alternative realities in the mind: the self that could have stayed behind in the old country, versus the one that went abroad for a new future. In this it is similar to the frantic, Oscar-winning multiverse comedy Everything Everywhere All at Once, though I think better and truer.

We start with a static shot of three adults, drinking uncomfortably in a New York bar: two are Korean, one is white American. A narrative voice, perhaps representing that of the audience or the film-maker, teasingly speculates as to who these people are. Flashbacks supply the answer: the first takes us to sometime in the late 1990s or early 2000s in Seoul, where a 12-year-old girl, Na-young (Seung Ah-moon), is walking home after school with a 12-year-old boy, Hae-sung (Seung Min-yim). They are sweethearts, though the relationship is clouded by competition, and the question of which of them will come first in the class. Na-young’s mother actually sets up a kind of romantic “play date” between the two, which fatally gives poor Hae-sung the impression that they are meant to be together, and his heart is broken when Na-young casually announces in class (not even directly to him) that her family is emigrating to North America.

The next section shows the two in their 20s: Na-young (played by Greta Lee) has anglicised her name to Nora and is now a budding literary star in New York. Poor, humble Hae-sung (Teo Yoo) is trudging through his military service back in Seoul and studying engineering. The two connect via Facebook and then Skype, and the beaming excitement of their conversations will have you on the edge of your seat. The movie screen is flooded with their happiness and a single unasked question: should they be together? Or is that illusory? Are they both romanticising the purity of their childhood friendship? A later section in New York has Na-young fully established in her prestigious career. Hae-sung, after a dismally failed relationship, finally comes to New York and meets Na-young and her husband, Arthur, (John Magaro), a promising novelist.

Lee’s brilliant code-switching between her Korean identity with Hae-sung and her American identity with Arthur is gripping, as is Magaro’s wary, pained questioning, as Arthur suspects (justifiably) that she is deeply in love with their Korean visitor. And as writers, Arthur and Na-young can see how Hae-sung, though a provincial country mouse compared to them, is actually incomparably more compelling and magnificent: a handsome, dignified, modest, heartbroken romantic hero who has sacrificed everything in his life for this distant real love.

Na-young/Nora talks about the Korean concept of “in-yun”, the karmic bringing together of people who were lovers in past lives. This wonderful film suggests a secular, 21st-century version: the past lives of Na-young and Hae-sung are their childhoods, preserved and exalted in their memory and by modern communications. Past Lives is a glorious date movie, and a movie for every occasion, too. As ever with films like this, there is an auxiliary pleasure in wondering how much of her own past life Song has used. It’s a must-see.

• Past Lives is released on 7 September in UK and Irish cinemas.