I would recommend using JavaScript's Audio().
Since audio is only loaded once the user interacts with the webpage, add a "click" event listener to the body to make sure the user has interacted with the webpage and then start playing the audio.

let audio = new Audio();
//Source goes here:
audio.src = "your_src.mp3"
document.body.addEventListener("click",function(){
  audio.play();
});

There you have it!

The best way to do this is put it in a separate file called "backgroundAudio.js" and link it into all your html files.