Form - Show partial form in block then populate full form with partial data
As contrib is an extension of core there are always ways to do stuff in core that you can do with contrib, it's just often contrib makes it easier, quicker, and more easily maintainable at the sacrifice of more code.

For this I would look at the prepopulate module which allows fields in most forms to be pre-populated from the $_REQUEST variable:

https://drupal.org/project/prepopulate

If you want to use just core then you know what you're outputting in the block, at a guess you could form_alter the form linked to prepopulate.