Automatic Display depends on the layout firing the content events, and many templates' blog overrides leave them out for intro items. The reliable way is a small override:

1. Copy

components/com_content/tmpl/category/blog_item.php

to

templates/<your template>/html/com_content/category/blog_item.php

2. Where you want the date, add:

<?php use Joomla\Component\Fields\Administrator\Helper\FieldsHelper; ?>

<?php foreach (FieldsHelper::getFields('com_content.article', $this->item, true) as $field) : ?>

    <?php if ($field->name === 'event-date') : ?>

        <p class="event-date"><?php echo $field->value; ?></p>

    <?php endif; ?>

<?php endforeach; ?>

With true the value comes back formatted by the field type. Use the field's name (alias), not its label.