"Welcome to Possible" is the slogan for Mindtree, a tech company based in India. There are dialect differences between Indian English and American or British English. I'm not sure if this is one of them.
In American English, the slogan is not grammatically correct. "Possible" is an adjective, but the slogan uses it as a noun. "Welcome to Possibilities" sounds more correct, but still a bit weird.
Slogans do not have to be grammatically correct. Their goal is to spread feelings, not information. They are vague and abstract by design. Another example like Mindtree's is the slogan for Microsoft's Zune music player, "Welcome to the Social" (adjective -> noun). There's also Apple's classic slogan, "Think Different" (adjective -> adverb). The grammar is wrong, but the meaning is clear.