He was one of the main influences of the later philosophers in the post WWII era, and Sartre did a lot of refrencing to him in a lot of his earlier work, even if they definitely did not see eye to eye on many things - he was a proto existentialist.
Friedrich Nietzsche is widely considered to be one of multiple early existentialist thinkers. Though Nietzsche never used the term 'existentialism' his work and philosophy is considered, together with Soren Kierkegaard, to be fundamental to the later existentialist movement. Thus it is correct to refer t Nietzsche as an early propnent of existentialism.
Friedrich Nietzsche is certainly a forefather to existentialism, as he was the first one to propose that we could very well just be brains floating around in jars. We have absolutely no way to prove that we are not, so we very well could be. This is the father to a lot of modern day philosophies and moves.
Everything about Fredrich Nietzsche's philosophy screamed existentialism. I am not sure that he has ever used the word existentialism, but much of his philosophy was very much existentialism. He believed that we can make our own rules and our own morality and decide what is good or not for ourselves which are some tenants of existentialism.
A rose is still a rose by any other name right? Can existentialism be just that even if Friedrich Nietzsche did not directly call it that. His ideas that the world around us requires us to conform to its values rather than allow us to develop our own values passes the test of existentialism, he just never developed that word, or a translatable word. The idea is the same.