There are some cases where there are symbols that experts can’t definitively agree are or are not writing. Maybe the symbols are just decoration.
Vinca is one such script, found on pottery and figurines in modern-day Serbia and adjoining countries . Artifacts with Vinca symbols on them have been dated to 5300BC — well before Egyptian hieroglyphics or Sumerian cuneiform. Unfortunately, nobody knows the language and there aren’t many symbols together (think “words” or “phrases” and not “paragraph” or “pages”), so it isn’t likely that we will ever decipher the writing system — if it is writing.
Many of the symbols are on the bottom of pottery, where in modern times it is common to see manufacturer’s marks. However, the same symbols show up over quite a large geographical range, so it’s not likely that it’s the 5300 BC version of CORELLE. It doesn’t seem likely that it was something thanking the gods for the food, or it would go on the front. It might be that the symbols say things like “Misha thanks Goddess Anomotoriabia for guidance in throwing this pot”, or that they are just pretty decoration.
Part of me feels that because writing is so incredibly useful, that if it were really writing, it would have persisted. On the other hand, it might be that your society needs to have a certain level of complexity for people to care about preserving information: Bob and Joe don’t need to agree on how many sheep Joe will bring back from the market if there is no market. Throw in war and disease, and it becomes easier to believe that writing could die out there.
A bigger objection I have is that the symbols mostly don’t look like pictures. In the three places where writing has unarguably developed (China, Central America, and the Middle East), the first writing looked like pictures. I can easily recognize ox heads, feet, snakes, horses, ears of corn, etc. in those scripts, while Vinca is much more abstract. Yes, it is true that cuneiform stylized, but the stylization came AFTER writing became quite well-established. Yes, it is possible that the Vincans developed a pictoral writing system first on materials that all decomposed, but humans are pretty egotistical, and I would have expected them to leave more permanent records of that stage of the script.