There is indeed no audible "pour se" at the beginning of the sentence. A lazy answer dropping it is not impossible but I would expect at least S’changer les idées…

Another explanation might just be a soundtrack editing problem, especially as the onset of changer sounds a little weird.

In any case, the end of the sentence is constructed in a way that makes the lack of pour se not grammatical, so it’s reasonable for a written transcription to keep it.

I’m pretty sure this is just some issue with audio editing of this recording. This is obviously an edited track, and it seems the person assembling these bits of audio together just started this bit (containing the answer) a bit too late, accidentally dropping the "pour se" part in the start. Which gets "corrected" in the transcript.

I’ve listened several times carefully, and it seems more and more obvious there was something said before as start of the answer is very abrupt, just as it would be if you start the recording in the middle of a sentence.

This is obviously a technical issue, and we hear a blank/pause instead of pour se. The target audience and slow speech is incompatible with reduction and reduction wouldn’t result in dropping pour se anyways; rather, some sounds would drop. The preposition pour is central to the turn of phrase here and the reflexive pronoun se is essential to leveraging the pronominal transitive use of the verb (se) changer with idées.