Your application will run as a non-root user, so it will not have the ability to install packages, at least in the traditional way. If you want to install a package, you can use the Apt Buildpack to install it. This will install the package, but into a location that does not require root access. It then adjusts your environment variables so that binaries & libraries can be found properly.
Also keep in mind that tasks are associated with an application (they both use the same droplet), so to make this work you'd need to do one of two things:
1.) Use multi-buildpacks to run the Apt buildpack plus your standard buildpack. This will produce a droplet that has both your required packages and your app bits. Then you can start your app and kick of tasks to set up the DB.
2.) Use two separate apps. One for your actual app and one for your code that seeds the database.
Either one should work though. Both are valid ways to seed your database. The other option, which is what I typically done, is to use some sort of tool to do this. Some frameworks like Rails, have this built-in. If your framework does not, you could bring your own tool, like Flyway. These tools often also help with the evolution of your DB schema, which can be useful too.
