You can get all JSON-LD blocks with
document.querySelectorAll('script[type="application/ld+json"]');
or just the first one with
document.querySelector('script[type="application/ld+json"]');
Here's a full example:
var jsonld = JSON.parse(document.querySelector('script[type="application/ld+json"]').innerText);
document.getElementById('result').innerText = jsonld.endDate;
<html>
<head>
<script type="application/ld+json">
{
"@context": "http://schema.org",
"@type": "Event",
"name": "A random event",
"startDate": "2013-09-14T21:30",
"endDate": "2013-09-14T21:30"
}
</script>
</head>
<body>
<p>The end date is: <strong id="result"></strong></p>
</body>
</html>