If you were to join StartupSchool which is an online incubator and is free to join you can get $1000 USD in AWS Credits which should for a small startup last you the full year. There are various other online incubators so it not super hard to get free credits to start working with.
If you have more time than money than Serverless architecture is free, ApiGateway, CloudFront, AWS Lambda, even SSL integration with Amazon Certification Manager is free where your usage you can have 1000 of users and maybe you will see a bill in the cents not even dollars.
If you really want simplicity just deploy to heroku, it can handle much but it will get the job done.
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