I'm aware of the background which lead to the discovery of the Americas/Other places and that it was preceded by centuries of several tries, before the Portuguese and Castillians, there was the Italians who developped several of the tools ( ex : https://en.wikipedia.org/wiki/Portolan_chart ) , techniques and methods of colonization/navigation in general over a long period of time during the Middle ages which made Christopher Columbus and the other explorers possible in the first place. So it did not come out of nowhere.
My question is : Was it necessary that Europeans discover these first ? Weren't the Muslim Berber dynasties (And Islamic in general) of Iberia and North/West Africa doing these types of discoveries themselves for example ?
Were the Western Europeans really the only ones exploring ?
Well, you sort of determine your answer by the way you frame your question.
Polynesians had their own extraordinary explorations and navigation to distant shores -- over a rather short time, they navigate enormous distances of open ocean in the Pacific. That's a pretty impressive "Age of Discovery". The distance from New Zealand/Aotearoa to Easter Island/Rapanui is about 7,000 kilometers; there are Polynesians in both places, speaking very similar languages, arriving about the same time (probably got to Rapa Nui a little earlier, but its within a few hundred years at most)
And when the ancestors of native Americans arrive in North America on the order of 15,000 years ago-- it takes them almost no time to spread out across the continent, head through Central America explore deep into the Amazon jungles, and get all the way to Tierra del Fuego by about 8000 years ago (latest date/first confirmed evidence).
Aboriginal Australians get to Australia some 65,000 years before anyone else does, and very quickly they're all over Oz, and find their way to Tasmania. I'd say that discovering a continent 65,000 years before anyone else ranks as impressive.
So all sorts of places-- much of the world, in fact-- was "discovered" by someone else, not European, first. The European discoveries come at the same time as a revolution in technology, so the effects are different . . . but it's a narrow view that doesn't see the remarkable breadth of "discovery" across human history. "Discovering" is what humans have been doing, since the time we became human.
Sources:POLYNESIAN NAVIGATION TO DISTANT ISLANDS
Polynesian Migration Voyages: Accidental or Purposeful
Complex processes in the settling of the Americas
Ancient mitochondrial DNA provides high-resolution time scale of the peopling of the Americas
A genomic history of Aboriginal Australia