Populate Javascript code with value from WordPress Custom Field?

If I were you, I’d store the GPS coordinates in the post meta. Maybe display a meta box on the edit pages, if you want to change it. Otherwise, add the post meta once and forget about it.

Then you can use the wp_footer hook to print the javascript with the post meta value as the coordinate.

namespace StackExchange\WordPress;

add_action( 'wp_footer', __NAMESPACE__ . '\wp_footer' );
function wp_footer() {
    echo '<script>var map = new mapboxgl.Map('.
    wp_json_encode( [ 'container' => 'map', 'center' => \get_post_meta( \get_the_ID() 'gpsCoordinates', true ) ])
        .');</script>';
}

If there’s already a named script enqueued that contains the code for mapboxgl, then you can just add an inline script.

namespace StackExchange\WordPress;

add_action( 'wp_enqueue_scripts', __NAMESPACE__ . 'wp_enqueue_scripts' );
function wp_enqueue_scripts() {
    wp_add_inline_script( 'mapbox', 
        'var map = new mapboxgl.Map('.
            wp_json_encode( [ 'container' => 'map', 'center' => \get_post_meta( \get_the_ID() 'gpsCoordinates', true ) ])
        .');'
    );
}

Have a look at the documentation for how to add meta boxes, if you don’t know already.