Heroku Postgres does provide a 'free tier' database option that you can use when you're developing applications before they launch.
To use the 'free tier' database, you can provision the addon like you would any other:
$ heroku addons:create heroku-postgresql # this is the free plan, by default
When your application is ready to go live, you can then backup your free database, provision a new, larger paid database, then import your data.
Heroku provides tools and documentation to do all of this in a very straight-forward way.