This works for me on Ubuntu 22.10:

  $ sudo apt install podman buildah
  $ mkdir empty && cd empty
  $ cat > Containerfile <<EOF
  FROM alpine:3.14
  RUN echo 'echo hello podman!' > /root/hello.sh
  ENTRYPOINT ["/bin/sh", "/root/hello.sh"]
  EOF
  $ buildah build -f Containerfile -t hello-podman .
  $ podman run -it --rm  localhost/hello-podman:latest
  hello podman!

edit: stryan has more minimalist instructions above.