Thanks for reaching out.
In fact, it is not possible to set first_publication_date using the Import/Export feature, and In fact, I will create a feature request and send it to our @features-team to allow that as it makes total sense.
A workaround would be to add a new field to your custom type, such as
publication_date and run a script to change it automatically in your WordPress export.
And then, you can have a fallback in your application to check if this field is set. You take its value. Otherwise, you accept the
first_publication_date to handle newly-created posts.
Please let us know if need any further help,