My mother passed away last month, and in a combination of honoring what we think my mother would have wanted, and what my sister wanted to get some closure, she was embalmed (at least I think she was), we had an open-casket funeral, and she was cremated shortly thereafter without being bured.
So it certainly is possible.
As for writing this scenario into your book, many deceased people have a safe-deposit box, but it’s not always known.
In my mother’s case, we knew she had one, we immediately opened it, and we found her will, as well as a letter (also signed by her attorney) indicating what she would want if she were to become incapacitated (like Terry Schiavo). We unfortunately didn’t find any funeral wishes, however.
Perhaps your story could include a family member finding out about the safe deposit box only several days after the character’s death, and upon opening it, find a letter by the deceased that she would prefer to be cremated, and/or was terrified of being buried.
Also, some people pre-pay for their entire funeral with a local funeral home, but not everyone knows about this. You might write into your story that it’s been discovered that the deceased had a prepaid funeral, which was only discovered a little too late, and that it specifically included cremation.
Another option, if your character was religous, would be perhaps find a religion that’s against burial, and have a pastor or other churchgoer come forward to object to the burial.