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.
Yes, I've used several of these modules myself. They save tons of time! Unfortunately, for legacy projects, I inherited a bunch of code from individuals that built everything "by hand" then copy-pasted everything. No re-usability.
PaaS is probably the way to go for small apps.