INSERT INTO table_name (date_column) VALUES (FROM_UNIXTIME(RAND() * UNIX_TIMESTAMP(),'%Y-%m-%d'));

CREATE TABLE test_table (
  id INT PRIMARY KEY AUTO_INCREMENT,
  name VARCHAR(50) NOT NULL,
  birth_date DATE NOT NULL
);

INSERT INTO test_table (name, birth_date)
VALUES
  ('Lucy', FROM_UNIXTIME(RAND() * UNIX_TIMESTAMP(),'%Y-%m-%d')),
  ('Tom', FROM_UNIXTIME(RAND() * UNIX_TIMESTAMP(),'%Y-%m-%d')),
  ('Lily', FROM_UNIXTIME(RAND() * UNIX_TIMESTAMP(),'%Y-%m-%d')),
  ('Jack', FROM_UNIXTIME(RAND() * UNIX_TIMESTAMP(),'%Y-%m-%d'));

SELECT * FROM test_table;

UPDATE table_name SET date_column=FROM_UNIXTIME(RAND() * UNIX_TIMESTAMP(),'%Y-%m-%d') WHERE condition;

UPDATE test_table SET birth_date=FROM_UNIXTIME(RAND() * UNIX_TIMESTAMP(),'%Y-%m-%d') WHERE id=1;

SELECT * FROM test_table;