Here is another very common post on the Exchange forum by many new Exchange Admin that they have setup/installed the Exchange but they can’t send the emails. The reason is simple that you need to setup a very first send connector for your outbound email flow
Open the Exchange Admin Center —goto Mail Flow — Send Connector
Click the PLUS + button to create a ‘new send connector’
Give a suitable name to the connector – in my case it is INTERNET
Click Next and the screen below show that you need to type the name of FQDN. We will set it up as * so it can send out email to any domain on the internet. Then SAVE
Below select the source server- I have two servers in this case and i’m going to add both of them
and here it is when you are done with creating the send connector – it is time to test your outbound emails.