Use output of wp_dropdown_categories($args)

wp_dropdown_categories() will produce a select element with the default name and id of cat. You can change these by passing different values for id and cat in the $args array. The default value it uses is the term_id. Depending on what you’re expected to use in the get_field() function, you can also change that in the $args array.

$args = array(
  'taxonomy'    => 'download_category',
  'order'       => 'ASC',
  'value_field' => 'slug',
);

Then in the second part:

$cat = esc_attr( $_GET[ 'cat' ] );
$product_args = array(
  'post_type'         => 'download',
  'posts_per_page'    => $per_page,
  'offset'            => $offset,
  'download_category' => $cat,
);

I’ve never combined ACF and EDD this way, so it might need some fiddling.