Is it permissible for a woman to marry without a guardian, especially if she has children and her previous marriage is not known?

Marriage is not valid except with a guardian (wali), for a woman does not have the authority to marry herself or anyone else, nor to appoint anyone other than her guardian, whether she has been married before or not. This is based on Allah's saying: "And marry the unmarried among you" (Quran 24:32), and "And do not marry polytheistic women until they believe" (Quran 2:221), and "So do not prevent them from marrying their [former] husbands" (Quran 2:232). And based on the saying of the Prophet (peace be upon him): "There is no marriage except with a guardian," and "Any woman who marries without the permission of her guardian, her marriage is invalid," and "A woman does not marry off another woman, nor does a woman marry herself off, for only the adulteress marries herself off." This is the view of the majority of scholars, both predecessors and successors.