The optimization process and recommendations:

1. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.

Optimal indexes for this query:

CREATE INDEX order_idx_orderdate ON order (orderDate);
CREATE INDEX person_idx_id_company_id ON person (id,company_id);
CREATE INDEX person_idx_company_id_id ON person (company_id,id);

The optimized query:

SELECT
        DISTINCT p1.company_id 
    FROM
        
    order o JOIN
        person p1 
            ON (
                o.person_id = p1.id 
                AND p1.company_id IS NOT NULL
            ) 
    WHERE
        o.orderDate > '2017-01-01' 
        AND o.orderDate < '2017-09-01' 
        AND NOT EXISTS (
            SELECT
                p2.company_id 
            FROM
                
            order o2 JOIN
                person p2 
                    ON (
                        o2.person_id = p2.id 
                        AND p2.company_id = p1.company_id
                    ) 
            WHERE
                o2.orderDate < '2017-01-01'
        )