Is it permissible to perform Hajj solely, without having performed 'Umrah previously?

The 'Umrah is obligatory according to the more preponderant opinion. For someone who performs Hajj as a Mutamatti' (combining Hajj and 'Umrah with a break in between) or a Qaarin (combining Hajj and 'Umrah without a break), their 'Umrah suffices for the 'Umrah of Islam. As for someone who performs Hajj as a Mufrid (Hajj only), it is permissible for them to do so, and then they perform the 'Umrah of Islam after completing the rituals of Hajj. They go out to the nearest point of the "Hill" (area outside the Haram boundary) and enter into Ihram for 'Umrah. This 'Umrah then suffices for the 'Umrah of Islam, and by doing so, they will have fulfilled the obligation, as Aisha (may Allah be pleased with her) did.