Dutch and other resident entrepreneurs that are registered with the Dutch Chamber of Commerce (Kamer van Koophandel, KVK) need to purchase eHerkenning (eRecognition) (i.e. electronic identification) first before creating their Message Box account. There is no other way. Recognised eHerkenning providers in the Netherlands offer various security levels for electronic identification. To open a Message Box account you will need at least security level 2+.
If you want to receive messages from Dutch government organisations, you should register your Message Box account in the Dutch Commercial Register. To do so, you can use the KVK's change of registration form.
Foreign entrepreneurs cannot use Dutch eHerkenning tools. To purchase eHerkenning, registration in the Dutch Commercial Register is mandatory and for most entrepreneurs this will not be useful or even possible. Therefore, foreign entrepreneurs need to register with Answers for Business, which is part of the Netherlands Enterprise Agency (Rijksdienst voor Ondernemend Nederland, RVO). This registration will then enable you to open a Message Box account.