Hi YTB,
I have checked your domain and DNS records, and I notice that you are an Office 365 P plan user.
How long have you added and verified your custom domain in Office 365? Typically it takes about 15 minutes for your changes take effect. But it can take up to 72 hours for the record that you created to update through the DNS system.
In the Office 365 MOP portal->Domains tab, you can change the SharePoint website address and point it to your custom domain.
The CNAME record is used for a subdirectory, it means you can add a CNAME record, host name is www, and points to your domain.com. But as you said, www.domain.com works well; I'd like to suggest you add another CNAME record, such as info (info.domain.com), and test it.
An A record is required, please contact the domain register and get more information.
Use a custom domain name for your SharePoint Online public-facing website address
Thanks,
Bourne Zhang