Is it obligatory to remain in the current job until a suitable opportunity in a desired field is found, or to leave it and trust in Allah while searching for a new job, knowing that the desired job holds a better future?

Do not leave your current permissible job before finding an alternative, for that is not reliance upon Allah but rather recklessness that may lead you to neglect your family. And remember the Prophet's (peace be upon him) saying: "It is enough sin for a man to neglect those whom he supports," and "Indeed, Allah loves that when one of you performs a deed, he perfects it."