How to filter only get rows that have the minimum/earliest date per group in a column with SQL

I am trying to filter a table in SQL so that only the rows that have the earliest date are kept per ID.

If I had the following table:

ID   Gender    Event_Date      
1     M        2015-03-01        
1     M        2012-04-15        
2     F        2005-11-14        
2     F        2005-11-14
2     F        2005-11-14
2     F        2013-05-19
2     F        2013-05-19
3     F        2010-07-02
3     F        2004-09-09
3     F        2004-02-17
3     F        2004-02-17
4     M        2019-01-29
5     M        2006-04-04
5     M        2006-08-07

And I would like to keep all of the rows that have the earliest date, when grouped by ID:

ID   Gender    Event_Date              
1     M        2012-04-15        
2     F        2005-11-14        
2     F        2005-11-14
2     F        2005-11-14
3     F        2004-02-17
3     F        2004-02-17
4     M        2019-01-29
5     M        2006-04-04

If I did the following:

SELECT * FROM table
GROUP BY ID
ORDER BY Event_Date ASC 
LIMIT 1;

How does LIMIT handle the ties? Would it keep all of the rows with earliest date or just pick one at random? (I want to keep all of them). I also tried versions of this:

SELECT * FROM table
WHERE Event_Date IS Min(Event_Date)

One canonical approach here would be to use the RANK() window function:

<!-- language: sql -->

WITH cte AS (
    SELECT t.*, RANK() OVER (PARTITION BY ID ORDER BY Event_Date) rnk
    FROM yourTable t
)

SELECT ID, Gender, Event_Date
FROM cte
WHERE rnk = 1
ORDER BY ID;

If your database does not have RANK(), then we can use exists logic:

<!-- language: sql -->

SELECT ID, Gender, Event_Date
FROM yourTable t1
WHERE NOT EXISTS (
    SELECT 1
    FROM yourTable t2
    WHERE t2.ID = t1.ID AND
          t2.Event_Date < t1.Event_Date
);