One significant thing to keep in mind regarding the newly-created German Empire was that it was essentially run by Otto von Bismarck. Yes, Kaiser Wilhelm I was the monarch and head of the Empire, but he trusted Bismarck and essentially listened to him on most matters (unlike his grandson would).
Bismarck was famously anti-colonies, something that could be surprising at first, since we think of Germany as constantly seeking 'its place in the sun.' He largely saw colonies as expensive and manpower-consuming investments that wouldn't necessarily pay off, as well as potential powder kegs for a European conflict, the avoidance of which was his primary objective from 1871-1890. Bismarck preferred to keep his attention at home, building up Germany into a powerhouse while maintaining a balance of power on the continent that isolated France, kept Russia docile, and prevented war. Actually, with French designs on Morocco he was interestingly cool with the idea, basically realizing that the French would be occupied with their new acquisition and perhaps not be as angry over the loss of Alsace-Lorraine at the conclusion of the Franco-Prussian War (obviously, this was only partially the case, as French revanchism was rampant from the early 1870s all the way to the outbreak of World War I in 1914).
He did, in the mid-1880s, begin going for small colonial gains in Africa and the South Pacific, but this largely seen as a way to appease the liberals and elites back home who clamored for overseas German supremacy.
With the ascension of Kaiser Wilhelm II in 1890 and the subsequent 'dropping the pilot' that followed, Bismarck left German politics & retired. The new Kaiser was significantly more hands-on, as well as much more aggressive in his foreign policy (he wanted a colonial empire like Britain & France), leading to increasing belligerence that pushed together the Triple Entente and laid the groundwork for the Great War.

Source(s): Hart, Peter. The Great War: A Combat History of the First World War. Oxford: Oxford University Press, 2015.
Bernadotte E. Schmitt, “Triple Alliance and Triple Entente, 1902-1914,” The American Historical Review 29, 3 (1924): 449-473
Fiona Tomaszewski, “Pomp, Circumstance, and Realpolitik: The Evolution of the Triple Entente of Russia, Great Britain, and France,” Jahrbücher für Geschichte Osteuropas 47, 3 (1999): 362-380

Your question comes out of a bad premise.

The Berlin Conference was called because Henry Morton Stanley had already been exploring and making deals with african chiefs and kings to create the sphere of influence for Leopold's Congo Society, since 1876.

Starting in 1879, and in response to Stanley and Leopold, the French sent Pierre Savorgnan de Brazza from their Gabon protectorate to explore and stake French claims of influence on the western side of the Congo river.

In addition to those claims, Portugal claimed the territory around the mouth of the Congo river, because they claimed a protectorate over the Kongo kingdom.

So, the Scramble for Africa was already underway, and the Berlin Conference was a response to these competing claims from the French, Portuguese, and Congo Society (Leopold). What the Conference did was establish a framework for recognizing the ways a power could exert "effective control" and could claim territory as a sphere of influence. (The conference also assured freedom of trade in the Congo basin for British, American, and other traders).

I included the year of German unification because the answer I know is that Germany arrived "too late" to the competition.

There is a lot of truth to the argument that Germany (and Italy, for that matter) was late to the competition.

If we take a look at these two maps, you'll notice that France already had colonies in 1880 along the coast in Algeria, Senegal, Gabon (marked as Congo), and on Reunion and Comoros Islands in the Indian Ocean. Similarly, in 1880 Great Britain had colonies in Gambia, Sierra Leone, the Gold Coast (Ghana) and Lagos in West Africa, as well as the Cape Colony in southern Africa. Finally, Portugal had her colonies at Cape Verde, Guinea, Angola and Mozambique.

So, as European interest in claiming territory in Africa increased, France and Britain were already poised with colonies on the coast to springboard into the interior.

Additionally, Britain and France both had long histories of sponsoring efforts at exploring the African interior, with Mungo Park exploring the Niger river to Timbuktu where he died in 1806, Rene Caille reaching Timbuktu in 1828 and returning alive to France, Hugh Clapperton crossing from Tripoli to Lake Chad from 1822-1827. David Livingstone exploring and prosletizing in a large part of central Africa from 1850-1873.

Of course, there were also ethnically German explorers and missionaries in Africa in the same era. Johannes Rebmann was the first European to describe the snow on Mt Kilimanjaro. Karl Mauch brought the ruins of Great Zimbabwe to public attention in 1871.

That long history of exploration provided Britain and France information about the geography of the African interior, and in the period of the Scramble for Africa, could draw on explorers like de Brazza to claim new lands for France or for Britain.