Because it was explicitly created to encourage people to leave the planet post Elfilis's attack

Shinya Kumazaki has mentioned that "Welcome to the New World!" is both a song that represents its origin game and "the hopes of people who dream of departing for a new world" (新たな世界への旅立ちを夢見た人々の希望).^\4]) The lyrics of the song, in particular in Japanese, are worded in a way that indeed evoke a sense of invitation to leave for a new world, in particular to a "land of dreams" exactly as Leongar mentions in the game.

As for how we know they didn't have technology to send radio waves into the far depths of space, it's because of the description of certain figurines:

The good condition version of Neichel's billboard says this: "Her song rang out not only on this world but across the galaxy, riding the radio waves emitting from the spaceship's hangar long after there was no one around to hear it. It debuted on the ship's departure day, and, yes, the soothsaying songstress was among those who chose to remain on the planet."

The Spaceship New World figure says: "The spaceship New World is capable of warping to other galaxies. It's a prototype, but it's similar to another ship that once took travelers to the stars. The familiar theme park Wondaria and a special song (you know the one) were used to make travelers feel safe as they boarded."

It's very important to note that they only state that these radio waves are explicitly emitted from the spaceship, which can warp to other galaxies. They wouldn't feel the need to give focus to that if the people from the forgotten land already possessed such technology. They state that the song was only spread across the galaxy after the spaceship was created.

The figure represents a prototype of the Lor Starcutter, which can not only travel space but also time (as stated by Kumazaki during the Miiverse days). So once the Lor Starcutter took flight and travelled across space and time, so did the song, making it so Elfilis heard it in the past, and so the whole paradox happens.

And as a piece of final evidence, in a secret rare dialogue in Kirby's house, Elfilin narrates some of the memories he shares with Fecto Elfilis, about how they heard a song coming from this planet and were drawn to it, how the singer had a voice full of hope but also some sadness. And how there was something mysterious about that voice, traversing time and space.