Is there an English word to describe when a sound "protrudes"?

I was going to go with "protrude" but I'm getting told it is not used in this sense and it wouldn't be understood.

It's to describe the situation where the TV is on but you are doing something else and not paying attention, so the sound is like a white noise to you. Then there is something important being said and you realize that suddenly you're hearing what's being said too, even though you didn't consciously make an effort to start listening. So the sensation is as if the sound emerged out of the white noise.

Best alternative I found is "suddenly becomes prominent", which I don't really like. Is there any other way to describe this?

It suddenly intruded upon my attention.

From the Journal of the Acoustical Society of America, courtesy Phil Sweet:

The extent to which an intruding noise source penetrates the general ambient noise environment in a community, serves as a useful indicator of the likely reaction of the community to that noise source. Available techniques using this approach generally provide a measure of community response based upon the absolute difference in level between the intruding and the ambient noise. Such techniques rarely take account of the percentage time for which the intruding noise is audible within the ambient...

I think part of what is confusing is the use of in a comment.

stick out (intr) 2 word verb

informal to be very easy to notice:

Cambridge online

That is pretty much idiomatic. What is actually happening is that the sound is sticking into your brain, and so intruding.

Intrude

to go into a place or situation in which you are not wanted or not expected to be:

In answer to your body question, which you expand upon in the tags you choose, there is the transitive multi-word verb jump out at, though I'd rate this as slightly informal.

jump out at: phrasal verb [transitive] ...

jump out at someone: if something jumps out at you, you notice it immediately

[Macmillan]

So The announcement of the Cricket World Cup result really jumped out at me.

An example from the internet:

Apr '14

The first whole sentence I understood on Radio Cymru: “Mae Mel Smith wedi marw”. Only three words of Welsh, I know, but they had jumped out at me while I was driving along not really listening. Sad for Mel Smith though…

[SSi_Forum_Exciting stages of language learning {helenlindsay}]

I would use interrupt and catch one's attention:

[Merriam-Webster]

interrupt
1 : to stop or hinder by breaking in
// interrupted the speaker with frequent questions
2 : to break the uniformity or continuity of
// a hot spell occasionally interrupted by a period of cool weather

grab/catch one's attention
: to cause one to become interested in something
// The book's title grabbed/caught my attention and I picked the book up.

As in:

I had been ignoring the background noise of the TV, when, suddenly, the breaking news story interrupted my thoughts, and caught my attention.