Optimizing a recursive CTE or replacing it with a temporary table

I have a recursive query like this:

with recursive PCte(id) as 
(
    select p1.id from Product p1 where p1.parent_id is null and p1.serial_number in
    ('123', '124','125', 'n')
    union all
    select p2.id from Product p2 inner join PCte cte on p2.parent_id = cte.id
) 
select * 
from Product p 
left join Product psub on psub.parent_id = p.id 
where p.id in (select c.id from PCte c)

This query have a slow performance with a large number of children, are there any possible optimization ways? If it is possible to replace the recursive CTE with a temporary table, I would like to see an example, thanks a lot.