get_cat_ID() not wokring

get_cat_ID gets the ID of a category based on the name. “Category” is a specific taxonomy named category. You’re trying to get the ID of a Product Category (product_cat). You cannot use get_cat_ID() to get the ID of a custom taxonomy.

To do that you need to use get_term_by():

$product_cat = get_term_by( 'name', $cat_name, 'product_cat' );

if ( $product_cat ) {
    $thisCatID = $product_cat->term_id;
}

But, based on your code, you don’t need to be finding the ID. You already have it:

$cate_object = get_the_terms( $post->ID, 'product_cat' );
foreach( $cate_object as $cate ){
    $thisCatID = $cate->term_id; // This is the ID.

    $cat_array[] = $thisCatID;
}