What's the free solution to having a custom email domains for side projects (instead of gmail)?

I'd highly recommend Skiff (https://skiff.com/), they have a very generous plan that is free forever.

GODADDY you can find a free custom email domain there after purchasing an actual domain. Thank me later 💃

If you don't want additional mailbox. Try Cloudflare email routing. Basically you'll route all emails incoming at hello@example.com to your gmail id. Then you can continue the conversation with just clicking reply all. Though not good in perspective of branding but best option for getting started.

Thank you so much for the answers 🙏

Update, Skiff was acquired by Notion. My latest solution is: https://www.gmailify.com/