Is the aforementioned 'Urfi marriage considered valid, with a child born within two years, despite the absence of a Sharia-compliant صيغة (formula/wording) in the written contract and in the presence of family and witnesses?

For a marriage contract to be valid, it requires a verbal offer (ijab) and acceptance (qabul) from the woman's guardian (wali) and the man. According to the majority of scholars, merely writing and signing the contract without verbalizing the offer and acceptance is not valid, and if done this way, the contract must be renewed. As for the testimony of the woman's brothers regarding the marriage, it is valid and permissible, contrary to what some believe. Regarding not documenting the marriage to benefit from social security, this is impermissible due to the deception involved.