MySQL 8.0

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CREATE TABLE `student_info` 
    (`student_id` INT NOT NULL, 
    `date_registered` DATE DEFAULT NULL, 
    PRIMARY KEY (`student_id`));
    
    INSERT INTO `student_info` VALUES
    (255193, '2021-12-01'),(255194, '2021-12-01'),(255196, '2021-12-01'),
    (255198, '2021-12-01'),(255199, '2021-12-01'),(255200, '2021-12-01'),
    (255201, '2021-12-01'),(255203, '2021-12-01'),(255204, '2021-12-01'),
    (255205, '2021-12-01');
    -- Full dataset has 40979 records
    
    CREATE TABLE `student_engagement` 
    (`student_id` INT DEFAULT NULL, 
    `date_watched` DATE DEFAULT NULL);
    
    INSERT INTO `student_engagement` VALUES
    (255200, '2021-12-01'),(255201, '2021-12-02'),(255201, '2021-12-06'),
    (255201, '2021-12-08'),(255201, '2022-10-05'),(255203, '2022-03-08'),
    (255203, '2022-03-17'),(255203, '2022-03-23'),(255203, '2021-12-01'),
    (255203, '2022-01-25'),(255203, '2022-01-26'),(255203, '2022-01-27'),
    (255203, '2022-02-08'),(255203, '2022-02-09'),(255203, '2022-02-21'),
    (255203, '2022-02-22'),(255203, '2022-02-23'),(255204, '2021-12-01'),
    (255204, '2021-12-02'),(255204, '2021-12-03'),(255204, '2021-12-14'),
    (255204, '2021-12-17'),(255204, '2021-12-07'),(255204, '2021-12-05'),
    (255204, '2021-12-09'),(255204, '2021-12-23'),(255204, '2022-01-11'),
    (255204, '2022-01-18'),(255204, '2022-03-05'),(255204, '2022-06-19'),
    (255204, '2022-07-06'),(255204, '2021-12-04'),(255204, '2021-12-18'),
    (255204, '2021-12-20'),(255204, '2021-12-29'),(255204, '2022-03-28'),
    (255204, '2022-03-31'),(255204, '2022-07-17'),(255204, '2022-07-21'),
    (255204, '2022-07-31'),(255204, '2021-12-12'),(255204, '2021-12-13'),
    (255204, '2021-12-21'),(255204, '2021-12-27'),(255204, '2022-01-07'),
    (255204, '2021-12-08'),(255204, '2022-01-27'),(255205, '2021-12-01'),
    (255205, '2021-12-02'),(255205, '2021-12-07'),(255205, '2022-01-22'),
    (255205, '2022-04-05');
    -- Full dataset has 74246 records
    
    CREATE TABLE `student_purchases` 
    (`purchase_id` INT NOT NULL, 
    `student_id` INT DEFAULT NULL, 
    `date_purchased` DATE DEFAULT NULL, 
    PRIMARY KEY (`purchase_id`));
    
    INSERT INTO `student_purchases` VALUES
    (15055, 255201, '2021-12-01'),(15057, 255203, '2021-12-01'),
    (15059, 255204, '2021-12-01'),(15060, 255196, '2021-12-01');
    -- Full dataset has 5922 records

Records: 10  Duplicates: 0  Warnings: 0



Records: 52  Duplicates: 0  Warnings: 0



Records: 4  Duplicates: 0  Warnings: 0


/*Your base query returning 5 records*/
SELECT se.student_id,
           si.date_registered,
           MIN(se.date_watched) AS first_date_watched,
           MIN(sp.date_purchased) AS first_date_purchased
    FROM student_engagement se
      LEFT JOIN student_info si ON se.student_id = si.student_id
      LEFT JOIN student_purchases sp ON se.student_id = sp.student_id
    GROUP BY se.student_id
    ORDER BY- first_date_purchased DESC


student_id
date_registered
first_date_watched
first_date_purchased


255201
2021-12-01
2021-12-02
2021-12-01

255203
2021-12-01
2021-12-01
2021-12-01

255204
2021-12-01
2021-12-01
2021-12-01

255200
2021-12-01
2021-12-01
null

255205
2021-12-01
2021-12-01
null


/*Posible solution but it seems odd to me you want the nulls*/
SELECT se.student_id,
           si.date_registered,
           MIN(se.date_watched) AS first_date_watched,
           MIN(sp.date_purchased) AS first_date_purchased
    FROM student_engagement se
      LEFT JOIN student_info si ON se.student_id = si.student_id
      LEFT JOIN student_purchases sp ON se.student_id = sp.student_id
    GROUP BY se.student_id, si.date_registered
    HAVING first_date_purchased >= first_date_watched
     or first_date_purchased is null
      
    ORDER BY first_date_purchased DESC


student_id
date_registered
first_date_watched
first_date_purchased


255203
2021-12-01
2021-12-01
2021-12-01

255204
2021-12-01
2021-12-01
2021-12-01

255200
2021-12-01
2021-12-01
null

255205
2021-12-01
2021-12-01
null


/*or's can be slow so maybe this will be faster...*/
SELECT se.student_id,
           si.date_registered,
           MIN(se.date_watched) AS first_date_watched,
           MIN(sp.date_purchased) AS first_date_purchased
    FROM student_engagement se
      LEFT JOIN student_info si ON se.student_id = si.student_id
      LEFT JOIN student_purchases sp ON se.student_id = sp.student_id
    GROUP BY se.student_id, si.date_registered
    HAVING
      coalesce(first_date_purchased,first_date_watched) >= first_date_watched
    ORDER BY first_date_purchased DESC


student_id
date_registered
first_date_watched
first_date_purchased


255203
2021-12-01
2021-12-01
2021-12-01

255204
2021-12-01
2021-12-01
2021-12-01

255200
2021-12-01
2021-12-01
null

255205
2021-12-01
2021-12-01
null
student_id	date_registered	first_date_watched	first_date_purchased
255201	2021-12-01	2021-12-02	2021-12-01
255203	2021-12-01	2021-12-01	2021-12-01
255204	2021-12-01	2021-12-01	2021-12-01
255200	2021-12-01	2021-12-01	null
255205	2021-12-01	2021-12-01	null