Trigger to update a field automatically after insert

I have a user table, basically:

CREATE TABLE IF NOT EXISTS 'sistema'.'user' (
  'id_user' INT NOT NULL AUTO_INCREMENT COMMENT '',
  'hashed_id' VARCHAR(40) NOT NULL COMMENT '',
  'nome' VARCHAR(40) NOT NULL COMMENT '',
  'cpf' VARCHAR(15) NOT NULL COMMENT '',
  UNIQUE INDEX 'hashed_id_UNIQUE' ('hashed_id' ASC)  COMMENT '',
    ON DELETE NO ACTION
    ON UPDATE NO ACTION)
ENGINE = InnoDB;

I want to create a trigger for when a new user is created, hashed_id is updated with a code of 12 numbers or letters, and I still have to make sure that hash is unique, as long as it is not, generate other.

It would be something like this:

CREATE DEFINER = CURRENT_USER TRIGGER 'sistema'.'teste_BEFORE_INSERT' BEFORE
INSERT
ON
  'teste' FOR EACH ROW
BEGIN
SELECT
  @lid := LAST_INSERT_ID();
UPDATE
  'sistema'.'teste'
SET
  hashed_id = CONCAT(
    SUBSTRING(
      'ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789',
      RAND(
        @seed := ROUND(RAND(@lid) * 4294967296)
      ) * 36 + 1,
      1
    ),
    SUBSTRING(
      'ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789',
      RAND(
        @seed := ROUND(RAND(@seed) * 4294967296)
      ) * 36 + 1,
      1
    ),
    SUBSTRING(
      'ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789',
      RAND(
        @seed := ROUND(RAND(@seed) * 4294967296)
      ) * 36 + 1,
      1
    ),
    SUBSTRING(
      'ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789',
      RAND(
        @seed := ROUND(RAND(@seed) * 4294967296)
      ) * 36 + 1,
      1
    ),
    SUBSTRING(
      'ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789',
      RAND(
        @seed := ROUND(RAND(@seed) * 4294967296)
      ) * 36 + 1,
      1
    ),
    SUBSTRING(
      'ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789',
      RAND(
        @seed := ROUND(RAND(@seed) * 4294967296)
      ) * 36 + 1,
      1
    ),
    SUBSTRING(
      'ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789',
      RAND(
        @seed := ROUND(RAND(@seed) * 4294967296)
      ) * 36 + 1,
      1
    ),
    SUBSTRING(
      'ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789',
      RAND(@seed) * 36 + 1,
      1
    )
  )
WHERE
  id = @lid;
  END

This trigger scheme is from here