For me it got good as soon as I went through the first time portal.
It got great at the second visit to the past.
It became immortal at the first visit to the dark ages.
I find the first visit to the future to be a slog for the most part, although it has one of the strongest scenes in the game. Power through that segment and it gets better in a hurry.
Also, don’t play Chrono Trigger with the sound off until you can play the soundtrack in your head. The soundtrack doesn’t gently suggest atmosphere like a modern game. It sets the tone for the scene.