The transition to desert would have happened about 500 years earlier without the influence of hunter-gatherers and cattle-herders.

Evidence

Pastoralists may have delayed the desertification of the Sahara (Earth.com)

corroborated: 2 independent passages support this claim
XREF: connects to: Desertification forced ancient humans to domesticate cattle as a food resource. — Neil MacGregor, A History of the World in 100 Objects, 162; Pastoralism blossomed in the Sahara from around 1000 years before collapse; humans may have held back the Sahara desert by around 500 years. — Humans delayed the onset of the Sahara desert by 500 years

Pastoralism blossomed in the Sahara from around 1000 years before collapse; humans may have held back the Sahara desert by around 500 years. (similarity 0.94)
Pastoralism spread across the Sahara while it was still well-watered, and may have delayed desertification. (similarity 0.92)
Increasing human population and sustainable pastoralism did not accelerate—and may even have delayed—the decline of the Green Sahara. (similarity 0.91)
Around 4000 BP a climate change leading to desertification of the Sahara forced cattle and pastoralists southward. (similarity 0.89)
Using a climate-vegetation model, pastoralism in fact likely slowed the deterioration of orbitally-driven climate change. (similarity 0.84)
Pastoralism itself is argued to enhance devegetation and regime shifts in unbalanced ecosystems, contributing to desertification. (similarity 0.83)
Desertification forced ancient humans to domesticate cattle as a food resource. (similarity 0.82)
The earliest evidence of cattle domestication comes from the Eastern Sahara, where climatic desiccation advanced most rapidly. (similarity 0.81)
Nomads who roamed the Sahara millennia ago were the first to domesticate cattle. (similarity 0.78)