How can a young man complete half his deen while his siblings live with him in the same house, based on his mother’s recommendation to take care of them?

If you are able to combine marriage with caring for your siblings by securing separate housing for them or for yourself, or if the dwelling is spacious enough for separation, then this is more appropriate. However, if you cannot combine them, and you need to get married and fear falling into sin, then marriage is obligatory for you, and it is not permissible to prioritize providing for your siblings over marriage. But if you feel secure from sin and can be patient, then there is no objection to delaying marriage until your siblings no longer need your support.