Step one would be to create a DNS entry for a subdomain to send mail from your Discourse instance. Let’s assume you’re going to use ‘discourse.doubtion.com’. That means you’re going to be sending email from @discourse.doubtion.com
Mailgun
Sign up for MailGun and add discourse.doubtion.com as a domain. Leave the window open as it will show you what DNS records we’re going to need to add in the next step.
Namecheap
Open your DNS control panel to create the MX and TXT records. You use NameCheap so it’s at Namecheap.com • Login
Because your domain is already set up for GSuite your mail settings should already look like this:
Replicate the DNS entries from Mailgun here, you’re going to need to add two MX records for the discourse subdomain, a CNAME for email.discourse as a subdomain, and two TXT records.
Wait ~10 minutes after creating these records then return to the mailgun window and click to verify the DNS records. If you got any wrong it will let you know. Once you’ve verified your domain use the credentials provided by Mailgun in the setup screen.