Is it permissible in Islamic law to marry a girl who has recently converted to Islam without the knowledge of her non-Muslim family, who oppose her marriage, with the agreement to formalize the marriage later; and does not adhering to the waiting period agreed upon with the family constitute lying or betrayal?

If the father of the girl is an infidel (kafir), he has no guardianship over her. If she desires to marry and has no Muslim guardian, she should refer her case to Islamic centers. If none exist, she may appoint a just Muslim man to marry her off. If the marriage is concluded fulfilling all conditions, but is not announced, it does not fall under the prohibited secret marriage (zawaj as-sirr), and there is no harm in documenting it later. As for the agreement to delay for six months, if she wishes to expedite it, this is her interest, and she can be persuaded to wait to avoid alienating her family from Islam.