No authority decides whether or not an English word “exists”. Dictionaries try to document the language as used by educated native speakers, but English has the largest vocabulary of any language (nearly a million words), so most dictionaries don’t list every single word. Anyhow, “innovativeness” certainly does exist: https://www.merriam-webster.com/thesaurus/innovativeness

It's an unusual word, but it does exist. 'Innovation' and 'innovativeness' are both correct words, but they have different meanings: 'Innovation' refers either to the product/idea/method itself, or to the process of developing it. 'Innovativeness' refers to the quality of being innovative. For example, if you admire a company for an innovation, it means that you admire its new product or way of doing things; if you admire a company for its innovativeness, it means that you admire its ability to come up with and develop new ideas.

As a native speaker, I've never heard it, and wouldn't say it. In fact, it sounds weird to me.. :)

I have heard this word before. It means something very close in meaning to "ability to invent".

Thank you all so much for your precious help. After having done some more searching, I think I agree with the opinion that "innovativeness" truly does exist. I came up with this link, it's a online bookstore and the said word appears in a book on the website. So I think it's very likely to be an orthodox word. https://www.igi-global.com/dictionary/innovativeness/14715