You do not need a website simply to create an AWS account. However, if you plan to use Amazon SES for email sending, AWS asks for a Website URL when you request production access and move your SES account out of the sandbox. AWS uses this information to better understand your business and the type of emails you intend to send.
Having an active and relevant website associated with your sending domain can also help AWS understand that your business and email-sending use case are legitimate. AWS recommends verifying your sending domain before requesting production access, as this is a best practice and may help your production access request get approved faster.
If you do not have a traditional website, provide AWS with as much accurate information as possible about your business and email-sending use case. Clearly explain how you collect subscribers, what type of emails you send, and how you handle bounces, complaints, and unsubscribes.
Please note that AWS reviews each Amazon SES production access request individually, and providing a website or verified domain does not guarantee approval.