How do I pull the first image from the first entry of the first subcategory?
This should work!

This code is to pull the first image, from the first entry of the first sub category given that the 'slug' passed into the first set is your top level category.

    {# Get the category from the slug. This will return one CategoryModel #}
    {% set topCat = craft.categories.slug('someSlug').first() %}

    {# Get the first subcategory under the top level category using the getChildren() method on the category model.  #}
    {% set firstSubCat = topCat.getChildren().first() %}

    {# Grab the first entry under that category using the relatedTo function and appending the .first() method to return only one item. #}
    {% set firstEntry = craft.entries.relatedTo( firstSubCat ).first()  %}

    {# Set your image from your asset field #}
    {% set image = firstEntry.assetField.first() %}