SELECT 
    `final_table`.`time`
  FROM
  `final_table`,
    `t_1`,
    `t_2` 
  WHERE `t_2`.`number` = 555  
    AND `t_2`.`id` = `t_1`.`t_2_id`
    AND `t_1`.`id` = `final_table`.`t_1_id`

SELECT 
    `final_table`.`time`
  FROM
    `final_table` 
  WHERE `final_table`.`t_1_id` IN 
    (SELECT 
      `id` 
    FROM
      `t_1` 
    WHERE 
      `t_1`.`t_2_id` IN 
      (SELECT 
        `id` 
      FROM
        `t_2` 
      WHERE `t_2`.`number` = 555))

...FROM final_table 
INNER JOIN table_1 ON final_table.t_1_id = t_1.id  
INNER JOIN t_2 ON  t_1.t_2.id = t_2.id WHERE t_2.number = 555