There is no fine tuning of tts or audio in ANKI. General setting for automatic sound playback: Deck Options - Anki Manual
The only thing I can offer you is to play the silence audio file before the audio. Then you will have time to think before the audio prompts are played.
I’m not sure whether AnkiDroid could add this feature – but I did note that in AnkiDesktop, audio and hint fields are incompatible.
It is not currently possible to use a hint field for audio — the audio will play regardless of whether you’ve clicked on the hint link. Field Replacements - Anki Manual