Does Simple Mail Service receiving need a mail server to work?

Hi,

I want to use the AWS SMS to monitor and process the inbound emails to an address like inbound@<mydomain>.com. I don't have any email server for this domain except for AWS SMS.

I have done the below

• Verified domain name.
• Created the MX record. I'm in Sydney, the MX record value is "10 inbound-smtp.ap-southeast-2.amazonaws.com"
• Create a general rule to save all the incoming email to S3.

However, the test email goes nowhere. When I tried to send an email from my gmail to this address, it bounced back with error "DNS type 'mx' lookup of <mydomain>.com responded with code NXDOMAIN Domain name not found:"

Is there anything missing? or I should also setup a real email server like AWS workmail?

Thanks,