How can my app prevent headsets from skipping the first fraction of a second when speaking text?

I first noticed the issue when listening to audiobooks on a new headset. Chapters and parts start systematically by …pter nine or …art two: the first fraction of a second is cut off. It also occurs on the first word at the start of some other paragraphs, seemingly when the narrator starts a new recording. I first thought this audiobook had a poor recording, but then I noticed it on other audiobooks, and also on podcasts and audio editions of a newspaper, in several different languages. It occurs on different apps, like Audible, The Economist, or (books narrated on) Apple Music, but not on all (f.i. not on audiobooks on Spotify). It never occurs on music, streamed spoken live radio, or time-shifted radio. It occurs on the Audible apps on both iOS and Android, but not on iOS VoiceOver announcements.

And it occurs on an app I developed that emits generated spoken text. Scheduling a pause before the speaking does not help. The VoiceOver UI of this and my other apps are not affected.

So far only a particular headset, an inexpensive bone-conducting Bluetooth model, shows this issue. None of my other headsets or Bluetooth speakers show the issue, and I didn’t notice it on another, even cheaper bone-conducting headset that I lost and replaced by this headset.

I could write this off as just a quality issue with that particular headset, but I would like to know if anybody else has noticed such an effect, and might have an explanation for it. Apparently at least Spotify avoids the issue, and I would like to know how to avoid the effect in my own app.