Sure, Lambda is fine for that small app, but I once inherited a 100k/month mess of SQS, Step Functions, API Gateway, Cognito, Lambda, ECS, AppSync, S3 and Kinesis that made me want to go into carpentry.
It wasn't simple, it was't quick to make, it wasn't cheap, it wasn't fast, and no: it did not scale (because we reached the limit of Step Functions).