Squarespace actually puts the full blog post publication date on every blog page in a meta element with an itemprop='datePublished'. If you search for this item and get the content attribute, you can use this to inject into the published date element.
<script>
//only run the code after the dom has loaded
document.addEventListener('DOMContentLoaded', function() {
//get the blog post html item so that we can later replace this with the full published date
var pubdate = document.getElementsByClassName("blog-meta-item--date");
//get the published info from the meta property on the page
var datePublishedMeta = document.querySelector('meta[itemprop="datePublished"]');
for (var i = 0; i < pubdate.length; i++) {
if (datePublishedMeta){
//turn the meta date into a Date item so we can restyle it
var d = new Date(datePublishedMeta.getAttribute('content'));
//Set the dateStyle. I prefer 'long' to display the full month like March instead of Mar
pubdate[i].innerText = d.toLocaleString('default', {dateStyle: 'long'});
}
}
});
</script>