Is it permissible for my brother to postpone 'Umrah on the pretext that he will not be able to lower his gaze until after marriage, under the impression that his 'Umrah will not be accepted now?

Your brother is obligated to perform 'Umrah immediately if the conditions for its obligation and ability are met. 'Umrah is obligatory upon the one who is able, and this is the most preponderant opinion among scholars. This is indicated by Allah's saying: "{And complete the Hajj and 'Umrah}" (Quran 2:196), where 'Umrah is conjoined with Hajj, and by prophetic narrations such as the Prophet's command (peace be upon him) to perform Hajj and 'Umrah on behalf of an elderly father. As for his claim that 'Umrah will distract him from marriage and cause him to fall into looking at what is unlawful, this is from the whispers of Satan. It is his duty to lower his gaze in all circumstances, and hastening to perform 'Umrah may be a reason for his repentance from unrestrained gazing.