I am afraid that this is not possible at the moment. The official documentation does not state any information about adding a delay before the greeting message. Maybe you can try using an audio file instead of text-to-speech and add some silence at the beginning of the file.
You can manage your call queues and auto attendant greetings in Teams by following these steps:
- Select Settings and more at the top right of Teams, then Settings > Calls.
- Choose the auto attendant line to which you want to make changes.
- Select No greeting, Add a greeting message, or Play an audio file from the greeting dropdown menu.
- If Play an audio file is selected, upload the audio file with accepted formats.
- If Add a greeting message is selected, type a message.
- Select Save.
For more details about manage your call queue and auto attendant greetings in Microsoft Teams, you could refer to this article.
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