There are two ways of doing this.
This is the simplest option. First add your audio file to your Google Drive. Then:
Select the file in your Drive
Get the link to share the file using 'Copy Link' (see screenshot)
In Google Sites, open the page you want to add the audio to
Click on Insert
Embed
URL
Paste the link to your audio file
Insert
Done!
First add your audio file to your Google Drive. Then:
Open the file in your Drive
Open the three dots menu and select 'Open in new window'
From the new window open the three dots menu and select 'Embed Item...'
Copy the code given
In Google Sites, open the page you want to add the audio to
Click on Insert > Embed > Embed Code
Paste in the code. (Modify code as required)
(I have set width = "440" height="70" in my example)
Done!
<iframe src="https://drive.google.com/file/d/1nxk6hlCgP09fCLjLlAC8ggYwaf-716xh/preview" width="440" height="70" allow="autoplay"></iframe>