If your hosting provider does not provide a SMTP server, you are on your own. There are several ways to send out emails from Moodle. One is set up your own mail server but this is difficult to install and maintain.
A better way requires a email account from yandex.com ( free) and ability to edit the CNAME record on the DNS domain record for your site.
Once you have a Yandex email account, log in and refer to the sign up for Yandex.Mail for Domain. When asked for proof of domain ownership , Confirm ownership as shown here. Once you have set up your domain, you should be able to add email users eg firstname.lastname@example.org. Check by sending and receiving messages through Yandex. Perhaps this link explains it better.
Now go to Moodle and set up smtp.yandex.com:587 and TLS in the smtp configuration ( SSL should also work). If you use the email@example.com as your smtp username there is a mismatch between sender and site sending the email so messages are usually rejected as spam. Instead use your address firstname.lastname@example.org to send emails from mylittlemoodle.com.