Yes, it's not only possible, but fairly easy to do! Depending on which registrar you purchased your domain through, you may be able to have them host your email. That may be the easiest option, but your registrar could suck so I can't recommend that off-hand.

Third party providers, like mailbox.org, mailfence, proton, tuta, runbox, zoho and others can all host your email. You just need DNS records and proof it's your domain.

Below is a link to mailbox.org's guide on hosting with them.

I read a few different guides and it seemed like the most comprehensive. The steps should be fairly similar for every potential email host.

https://kb.mailbox.org/en/private/e-mail-article/using-e-mail-addresses-of-your-domain/