Once Two-Factor Authentication is enabled (or if you already had it enabled), then visit https://myaccount.google.com/apppasswords.
When prompted for "Select the app and device you want to generate the app password for":
Select "Mail" under the drop-down for "Select app"
Select "Other" under the drop-down for "Select device"
When prompted for text input, enter your custom domain's email address you're forwarding from (e.g. "[email protected]" - this will help you keep track in case you use this service for multiple accounts)
Copy the password to your clipboard that is automatically generatedImportant: If you are using G Suite, visit your admin panel Apps G Suite Settings for Gmail Advanced settings and make sure to check "Allow users to send mail through an external SMTP server...". There will be some delay for this change to be activated, so please wait a few minutes.
When prompted for "Name", enter the name that you want your email to be seen as "From" (e.g. "Elon Musk")
When prompted for "Email address", enter the email address with the custom domain you used above (e.g. "[email protected]")
Uncheck "Treat as an alias"
Click "Next Step" to proceed
When prompted for "SMTP Server"
smtp.gmail.com PORT 587 TLS
When prompted for "Password", paste from your clipboard the password you generated in step 2 above
Leave the radio button checked to "Secured connection using TLS"
Click "Add Account" to proceed
Open a new tab to Gmail and wait for your verification email to arrive (you will receive a verification code that confirms you are the owner of the email address you are attempting to "Send Mail As")
Once it arrives, copy and paste the verification code at the prompt you received in the previous step
Once you've done that, go back to the email and click the link to "confirm the request". You need to do this step and the previous step for the email to be correctly configured.
Congratulations! You've successfully completed all steps.