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My husband and I were talking about a song that part way through made us gasp because it was so amazing. He said to me "I need a word for when something is experienced for the first time, and you know it’s special, and nothing will ever be like that again."
Is there a word or phrase for this?

The phrase once-in-a-lifetime might be useful here. From Cambridge Dictionaries:

A once-in-a-lifetime experience or opportunity is very special because you will probably only have it once

So in your example, you could say something like

Hearing that song for the first time was a once-in-a-lifetime experience.

Even though this is literally true of anything you do or hear for the first time, the connotation is that the experience of hearing this particular song for the first time was so special in some way that even hearing the song a second time or hearing any other song for the first time won't match the feeling you got.

Perhaps "Miracle", particularly with the meaning of a unique unusual event, without the literal aspect of being impossible or supernatural, instead poetically expressed as "special".

Incomparable

[Merriam-Webster]

1 : eminent beyond comparison : MATCHLESS
2 : not suitable for comparison

It has the combined meaning of being unique (and, therefore, unrepeatable) and of a particularly noteworthy quality.

It's often used when discussing people who you want to praise as excelling in something and exhibiting qualities that have never been seen before. But it can also be applied to other things.

How about...

Transcendent

From the Oxford Dictionary:
"Beyond or above the range of normal or physical human experience"

The emotion you described feeling when you heard the song transcended what you had previously experienced before, and it's unlikely to be repeated to such a meaningful degree again.