Assuming  that you have no general issue with your SMTP server, keep in mind that the pluging uses the WP-Cron scheduler to send emails in small batches at regular intervals.

WP-Cron is a built-in cron job (wp-cron.php) in WordPress that runs every time someone visits the website.

In most cases emails will be delivered fast unless you have a website that has little traffic or a very large mailing list.

For websites with low traffic, we recommend to run wp-cron.php externally via Crontab.