A small app (or a larger one, for that matter) can quite easily run on infra that's instantiated from canned IaC, like TF AWS Modules [0]. If you can read docs, you should be able to quite trivially get some basic infra up in a day, even with zero prior experience managing it.

[0]: https://github.com/terraform-aws-modules

But that effort has a huge payoff in that it can be used to disaster recovery in a new region and to spin up testing environments.