For trying Mantil, you can for sure stay within free tier of all the AWS services. You have pretty generous monthly limits for many services when you create a new AWS account. The two most important you will use with Mantil are Lambda functions and API Gateway. Here are their free tier monthly limits:
The Amazon API Gateway free tier includes one million API calls received for REST APIs, one million API calls received for HTTP APIs, and one million messages and 750,000 connection minutes for WebSocket APIs per month for up to 12 months.
The AWS Lambda free tier includes one million free requests per month and 400,000 GB-seconds of compute time per month.
Until you don't have some significant user base or are not mining bitcoins in your Lambda function, you will for sure stay within the limits of the free tier. So trying Mantil will cost you nothing.