Hi makenzi.exc,
Initially set a variable to false.
Set the controls to false in audio element once played and set a variable to true.
Refer below example.
HTML
<!DOCTYPE html>
<html>
<head>
<meta charset="utf-8" />
<title></title>
<style type="text/css">
body { font-family: Arial; font-size: 10pt; }
</style>
</head>
<body>
<audio id="audio" controls onended="DisablePlay()">
<source src="https://www.aspsnippets.com/audio/welcome.mp3" type="audio/mpeg">
</audio>
<script type="text/javascript">
var audioPlayed = false;
function DisablePlay() {
var audio = document.getElementById('audio');
if (!audioPlayed) {
audio.controls = false;
audioPlayed = true;
}
}
</script>
</body>
</html>
Demo
Screenshot

Downloads
Download Sample