Set entity reference field to 'autocreate' directly in the entity field definitions
I finally found a way to get it to work after digging through the code for the EntityReferenceAutocompleteWidget. To enable automatic creation, I needed to edit the handler settings. Here's my code:

$fields['client'] = BaseFieldDefinition::create('entity_reference')
  -&gt;setLabel(t('Client'))
  -&gt;setSettings(array(
    'target_type'      =&gt; 'client',
    'handler'          =&gt; 'default',
    'handler_settings' =&gt; array(            // Added
      'auto_create'    =&gt; TRUE              // Added
    )
  ))
  -&gt;setDisplayOptions('form', array(
    'type'     =&gt; 'entity_reference_autocomplete',
    'settings' =&gt; array(
      'match_operator' =&gt; 'CONTAINS',
      'size'           =&gt; 60,
      'placeholder'    =&gt; ''
    ),
    'weight'   =&gt; 0
  ))
  -&gt;setRequired(TRUE);