I have now seen Angel's Egg twice, and it's a 10/10. What a stunning piece of art. I've formed what is IMO a fairly cohesive interpretation of it, which I will now share for your indifference:
What we see in the film is part of a larger chain of events, which could be called a creation myth. Or more accurately, a recreation myth, because the movie is depicting the rebirth of a world. You see, the world of the movie is post-apocalyptic, and in the most literal sense: the actual biblical apocalypse, God vs Lucifer, has come and gone. God won in the end, but through overwhelming cost that left the world and reality itself in ruin, and God is now in the process of starting the world anew through some unspeakably complex machination, which we see a part of in the movie. The title of the film is literal on multiple levels: the girl holding the egg is an angel, and the eggs suspended on what look like upwards-growing tree roots are holding the fetal forms of angels. The angels are slowly incubating, waiting for the day that they can awaken and start their phase of the rebuilding of the world.
The apocalypse of the world was so total and so thorough that reality itself broke apart. That's why there's all sorts of weird, unexplained shit. But reality is slowly being reconstructed through God's plan. In it lower ranks of angels, of whom the girl is one, are sent one by one to the world, have their memories wiped, and are tasked with protecting an egg for an unstated purpose. That's why, despite looking like a child, the girl doesn't really act like one, and is so protective of the egg: in the back of her mind she has a sense of assuredness, and the egg is the most precious thing in the world to her. The man she encounters is another angel: no other than Lucifer himself! He's been cast down into the world to inhabit a vessel, had his memories removed, and is serving his penance as the villain in God's plan. He is tasked with encountering the angels sent by God, gaining their trust, and one after another breaking the eggs they're protecting. Upon that betrayal, the breaking of spirit, and the ensuing burst of emotion, a small part of reality is restored, the angel is called back into heaven, and the cycle repeats.
Lucifer's penance lies in him slowly recovering his memories during these visits, which he will then lose upon completion, forced to betray his brothers and sisters in an endless cycle in this forgotten world. There is a line that's repeated three times in the movie (which is significant for how little dialogue there is): "Who are you?" It's both a reminder and a taunt towards Lucifer: as he remembers who he is time and time again, he is forced to confront his identity as the angel who destroyed the world. To rub salt in the wound he is forced to bear a twisted form of the Christian cross, as if God's saying "yeah, you know who's on top".
What of the shadowy men hunting the shadows of fish then? This is where I have to kind of start making leaps, but I interpreted them as the echoes of humanity: half-remembered forms of beings that once existed. The fish is one of the most significant symbols in Christianity, having all sorts of meanings: Jesus himself, the christian faith in general, the story of the five fish and two loaves of bread. You could derive any amount of interpretations of the film from that: maybe the fish are the presence of God himself, who's checking if the angel is proceeding with their task as planned. Maybe it's Jesus seeking to reconnect with humanity, being only met with scorn and rejection.
Then there's the water, which is a huge part of the film: one of the first locations the girl visits is a pond, there's rain, flooding, talk of the biblical flood of Noah and so on. This is another part where you could really slot in almost any meaning you want. To me the water signifies that the reclamation of the world during the film is quite a ways in: water after all is considered the foremost source of life, and one of the first sentences in the Bible is about how the spirit of God floated above the waters. So the water represents the promise of rebirth and life, and signifies God's presence.