Arabic DID exist sibnce long, it just would be a national-regional language, max.
Well, bad wording on my part for brevity's sake. Yes, Arabic existed (its earliest attested inscription is dated 328AD, iirc), but its subsequent evolution without Islam as a written language would be
way different; the grammatical codification of the Qur'anic phase, that provided the basis for Classical Arabic and Modern Standard Arabic, would not occur at all or be completely unrecognizable, substrate and adstrate influence on the spoken variants would change completely, and so on.
So, well, probably some form of Arabic would exist, and probably would exist as a written language to some extent at least. It is not likely that it would be a significant cultural language anywhere, and if so, it would be deeply changed in lexicon and probably, to some extent, grammar. There is no warrant that the pre-islamic poetry of that time will be preserved (and surely it wouldn't in an identical form, for obvious transmission matters). The time immediately preceding and following the Prophet's life was a key moment in the linguistic and literary canonization; the corpus of what is considered "arabic" OTL formed then.
A change there would impact heavily subsequent evolution.