Show button in header when product custom field is not empty

I would suggest two solutions.

Solution:1 Use WP_Query, if there are only few products, may be 10 or 20

Use WP_Query, loop through all the products, check if transmission_URL is not empty, if it is not empty, print the link and break from the loop.

The following code snippet goes inside header.php

$product_query = new WP_Query( array( 
  'post_type' => 'product' 
) );
if( $product_query->have_posts() ):
 while( $product_query->have_posts() ): $product_query->the_post();
   $transmissionURL = get_field('transmission_URL');
   if (! empty( $transmissionURL ) ) :
    echo '<a href="https://wordpress.stackexchange.com/questions/272458/URL-to-product-which-have-active-transmission" class="btn">LIVE</a>';
    break; // come out of while loop entirely, cause we are done.
   else:
    continue; // skip to the next product, stay inside while loop.
   endif;
 endwhile;
endif;

---

Solution 2: Make use of categories.

If the product count is high or If you want to save some maintenance time,

Create and assign a new category active-transmission to product_cat taxonomy. Then you can just query for the product with category active-transmission. This also allows to track previously transmission-ed product easily.

$product_query = new WP_Query( array( 
  'post_type' => 'product',
  'posts_per_page' => 1, // pull out only one product from the category
  'tax_query' => array(
        array(
            'taxonomy' => 'product_cat',
            'field'    => 'slug',
            'terms'    => 'active-transmission',
        ),
    ), 
) );
if( $product_query->have_posts() ):
 while( $product_query->have_posts() ): $product_query->the_post();
   $transmissionURL = get_field('transmission_URL');
   if (! empty( $transmissionURL ) ) :
    echo '<a href="https://wordpress.stackexchange.com/questions/272458/URL-to-product-which-have-active-transmission" class="btn">LIVE</a>';
   endif;
 endwhile;
endif;

You can modify the If blocks based on your requirements.