Is it permissible for the younger brother to marry before his elder brothers?

You are not too young to get married. Amr ibn al-Aas married when he was eleven years old. Rely on Allah and get married. Your elder brothers will get married when it becomes easy for them. It is a grave mistake not to marry off the youngest daughter when there are older ones, and this is forbidden. If a suitable man, in character and religiosity, proposes to her, then she should be married off. She might be an obstacle preventing the older sister from getting married, and if she marries, Allah will open the door for the older one. This marriage is not disobedience to parents nor a severing of ties with the two brothers.