A band is a fitting term for a small group that is basically an extended family who are part of a band society, a pre-tribalism community category normally used for typical prehistoric societies.
I have considered something along that line, but here's why I didn't go for
Hominids.
The Hominidae taxonomic family of primates whose members are called
Hominids (or Great Apes) include Pongo, Orangutang, Gorilla, and Pan in addition to the Homo genus.
The Homininae taxonomic subfamily of Hominidae whose members are called Hominines include Gorilla, and Pan in addition to the Homo genus.
The Hominini taxonomic tribe of the subfamily Homininae whose members are called Hominins include Pan (Chimpanzee and Bonobo) in addition to the Homo Genus.
The Australopithecina taxonomic subtribe of the tribe Hominini whose members are called Australopithecines (or Hominina) include Ardipithecus, Orrorin, Sahelanthropus, and Graecopithecus in addition to the Australopithecus genus.
From the Australopithecus genus the Paranthropus, Kenyanthropus, and the Homo genera evolved.
If we are to use a precise taxonomic term it should be as precise as possible, so a "Band of Homos", or a "Horde of Homos" would be more precise than
Hominids and Australopithecus.
Though that doesn't sound good to modern ears, so I would prefer "Ancestral Band", it's an unspecific generic term, it doesn't try to isolate a specific group, and imo it sounds good as a name of the initial unit.
End note: Earliest species of the Homo genus are H. Habilis, H. Erectus, H. Rudolfensis, H. Floresiensis, and Australopithecus sediba (last one may be a transitional species between Australopithecus and Homo).
H. Erectus is most likely the predecessor of H. Sapiens and H. Neanderthalensis.
On that note Band of Homo Erectus would be a name that would encompass both sapien and neanderthal, but that too doesn't sound good to modern ears.