First of all, the name Cushitic and the Kingdom of Kush have little to do with it each other. It was just some random name that was picked by early linguists. The Cushitic language family is much older than any Nubian civilization.
Secondly, there is no archeological nor genetic evidence of Cushites passing through Southern Sudan whatsoever. In fact, native populations in Southern Sudan are less Eurasian than even Nigerians and have less Neanderthal affinity than them. They were extremely separated from Cushites.
The consensus among geneticists is that Cushites passed through Northeastern Sudan, then Eritrea, then Northern Ethiopia. The Lowland East Cushitic branch likely first emerged around the Awash river or around Harar-Hargeisa-Hawd area.
East Africa is a strategic region to study human genetic diversity due to the presence of ethnically, linguistically and geographically diverse populations. Here, we provide new insight into the genetic history of populations living in the Sudanese region of East Africa by analysing nine ethnic...
www.nature.com
"Nubians are the only Nilo-Saharan speaking group that does not cluster with groups of the same linguistic affiliation, but with Sudanese Afro-Asiatic speaking groups (Arabs and Cushitic Beja) and Afro-Asiatic Ethiopians.
Y-chromosome and mitochondrial DNA studies reported Nubians to be more similar to Egyptians and Ethiopians than to other Nilo-Saharan populations.
The genetics of East African populations: a Nilo-Saharan component in the African genetic landscape
"A random subset of 18 individuals from each population was selected to avoid sample size bias. Columns represent individuals, where the size of each colour segment represents the proportion of ancestry from each cluster. Although k = 3 is the statistically supported model, here we show the results from k = 2 through k = 5 as they explain several ancestral components: North African/Middle Eastern (dark blue), Sub-Saharan (light blue), Coptic/Cushitic (dark green), Nilo-Saharan (light green) and Fulani (pink). MKK = Maasai from Kinyawa, Kenya; LWK = Luhya from Webuye, Kenya; YRI = Yoruba from Ibadan, Nigeria."
See the named authors for credentials:
"A number of extinct populations are thought to have spoken Afro-Asiatic languages of the Cushitic branch. According to Peter Behrens (1981) and Marianne Bechaus-Gerst (2000), linguistic evidence indicates that the peoples of the
Kerma Culture in present-day southern
Egypt and northern
Sudan spoke Cushitic languages.
The Nilo-Saharan
Nobiin language today contains a number of key pastoralism related
loanwords that are of proto-Highland East Cushitic origin, including the terms for sheep/goatskin, hen/cock, livestock enclosure, butter and milk. This in turn suggests that the Kerma population — which, along with the
C-Group culture, inhabited the Nile Valley immediately before the arrival of the first Nubian speakers — spoke Afro-Asiatic languages."
--------------------------------
In his 2011 book History and the testimony of language Ehret shows a map of Cushitic migration from the Red Sea Hills across Eritrea, etc into northern Somalia and the headwaters of the Jubba at 4-6000 BCE. This is most likely to have been the Southern and Highland Eastern Cushites as early northern inhabitants like the Dir, Harla, Yibir, the J1s, etc, are not Cushitic. In his Invention of Somalia maps he shows the Ahmar-Dharoor in the North in the 8th century and the Maxay speakers there only in the 14th century. Another of his maps in the Testimony of Language shows a very significant Highland Eastern Cushitic population just west of both the Jubba and Shebelle watersheds and covering the extreme southern Awash for the period 500 BC-100 AD
--------------------------------------------
Either the Lowland Eastern Cushites descend from Highland Eastern Cushites or we need to find another migration.