Amazon have been offering FREE Tier service for a year.
You can now grab using your own account without the need to setup an organization first.
You can see the detail of offering at https://aws.amazon.com/free
These are few recipes that I can gather for this purpose.
1. Register your own domain. Point it to a manageable DNS server.
I personally use namecheap. But there are also Free service provider such as Hurricane at https://dns.he.net that offer the similar capability.
2. Once the domain registered and propagated properly.
You should at least able to receive email on this domain by now.
3. Register AWS free tier with your new domain’s email.