Is it permissible to marry a previously married woman with a dowry, witnesses, and an Imam, without publicizing the marriage or official registration, and with the intention of facilitating divorce, in order to avoid falling into sin and to confront urgent sexual desires, while focusing on personal goals?

Legitimate marriage has conditions and pillars without which it is invalid. Among these is the guardian, without whom marriage is not valid according to the majority of scholars. Documenting the contract is not a condition for its validity, but neglecting it may lead to harm and loss of rights. If you are able to contract a valid marriage, then proceed with it, even if it means compromising on some matters, in order to preserve chastity and faith, and seek a religious spouse. If you are not able, then be patient and remain chaste, "And whoever fears Allah – He will make for him a way out, And will provide for him from where he does not expect." Avoid places of temptation, and seek a job free from unlawful mixing. You must also frequently fast, lower your gaze, and stay away from anything that arouses desire, while strengthening your connection with Allah and relying on Him, engaging in sports, occupying your time with what is beneficial, befriending the righteous, and persistent supplication.