I’m running the following query in BigQuery:

 WITH mock AS (
        SELECT 
            TIMESTAMP '2024-04-01 22:26:25' AS event_timestamp,
            'h6p2ylt679me5pcz' AS user_pseudo_id,
            'session start' AS event_name,
            1712010385 AS ga_session_id,
            'example.com' AS hostname
        UNION ALL
        SELECT 
            TIMESTAMP '2024-04-01 22:26:28' AS event_timestamp,
            'h6p2ylt679me5pcz' AS user_pseudo_id,
            'view' AS event_name,
            1712010385 AS ga_session_id,
            'example.com' AS hostname
        UNION ALL
        SELECT 
            TIMESTAMP '2024-04-01 22:26:31' AS event_timestamp,
            'h6p2ylt679me5pcz' AS user_pseudo_id,
            'click' AS event_name,
            1712010385 AS ga_session_id,
            'example.com' AS hostname
        UNION ALL
        SELECT 
            TIMESTAMP '2024-04-01 22:26:50' AS event_timestamp,
            'h6p2ylt679me5pcz' AS user_pseudo_id,
            'click' AS event_name,
            1712010385 AS ga_session_id,
            'example.com' AS hostname
        UNION ALL
        SELECT 
            TIMESTAMP '2024-04-01 22:27:02' AS event_timestamp,
            'h6p2ylt679me5pcz' AS user_pseudo_id,
            'session start' AS event_name,
            2939469694 AS ga_session_id,
            'example2.com' AS hostname
        UNION ALL
        SELECT 
            TIMESTAMP '2024-04-01 22:27:14' AS event_timestamp,
            'h6p2ylt679me5pcz' AS user_pseudo_id,
            'view' AS event_name,
            2939469694 AS ga_session_id,
            'example2.com' AS hostname
        UNION ALL
        SELECT 
            TIMESTAMP '2024-04-01 22:27:50' AS event_timestamp,
            'h6p2ylt679me5pcz' AS user_pseudo_id,
            'click' AS event_name,
            2939469694 AS ga_session_id,
            'example2.com' AS hostname
    ),
    
    raw AS (
        SELECT 
            event_timestamp,
            user_pseudo_id,
            event_name,
            hostname,
            ga_session_id,
            MIN(event_timestamp) OVER (PARTITION BY user_pseudo_id, ga_session_id) AS session_start
        FROM mock
    )
    
    SELECT 
        *, 
        LAG(ga_session_id) OVER (PARTITION BY user_pseudo_id ORDER BY session_start) AS ga_session_id_fix
    FROM raw
    ORDER BY event_timestamp ASC;

This is the output I have

| Row | event_timestamp          | user_pseudo_id      | event_name     | hostname      | ga_session_id | session_start          | ga_session_id_fix |
|-----|--------------------------|---------------------|----------------|---------------|---------------|------------------------|-------------------|
| 1   | 2024-04-01 22:26:25 UTC  | h6p2ylt679me5pcz    | session start  | example.com   | 1712010385    | 2024-04-01 22:26:25 UTC| null              |
| 2   | 2024-04-01 22:26:28 UTC  | h6p2ylt679me5pcz    | view           | example.com   | 1712010385    | 2024-04-01 22:26:25 UTC| 1712010385        |
| 3   | 2024-04-01 22:26:31 UTC  | h6p2ylt679me5pcz    | click          | example.com   | 1712010385    | 2024-04-01 22:26:25 UTC| 1712010385        |
| 4   | 2024-04-01 22:26:50 UTC  | h6p2ylt679me5pcz    | click          | example.com   | 1712010385    | 2024-04-01 22:26:25 UTC| 1712010385        |
| 5   | 2024-04-01 22:27:02 UTC  | h6p2ylt679me5pcz    | session start  | example2.com  | 2939469694    | 2024-04-01 22:27:02 UTC| 1712010385        |
| 6   | 2024-04-01 22:27:14 UTC  | h6p2ylt679me5pcz    | view           | example2.com  | 2939469694    | 2024-04-01 22:27:02 UTC| 2939469694        |
| 7   | 2024-04-01 22:27:50 UTC  | h6p2ylt679me5pcz    | click          | example2.com  | 2939469694    | 2024-04-01 22:27:02 UTC| 2939469694        |

Why the last two rows ga_session_id_fix column doesn’t return the session id of the first session.