By default, Google Groups are closed and require membership to email the group.  There are cases where this isn’t ideal, such as:

• using the email for social media accounts
• creating a department email that people from other organizations can email
• etc.

If you are using the group to receive public emails these settings.

Permissions > Basic permissions

• Post: Public

Settings > Moderation

• Spam messages: Skip the moderation queue and post to the group

The first setting is required and the second optional, but random legitimate messages tend to get caught in the Spam filters.