this is possible.Using a hole dug the day before by the cemetery for an early burial the next morning, and left unattended overnight has been speculated on forums over the years.
The general idea being that the body of SS could've been concealed in a preexisting grave on the night.
It's generally thought to be difficult to sleuth a list of possible gravesites by amateur detectives because MCB database via the website is not searchable by date of burial. I'd assume that is on the list of places that police have to go through, and there's probably many others.
I don't envy their chances as ground penetrating radar would be complicated due to the cemetery burying bodies on top of previous burials as plot leases expire. For example, the cemetery renewal program has seen a vast expansion of this practice. http://www.mcb.wa.gov.au/our-cemeteries/karrakatta-cemetery/cemetery-renewal
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As mentioned above, I found it hard to believe a full grave could be dug or a shallow grave not being uncovered. but what you propose is completely possible.
There are number of graves left open each night, with loads of soft sand nearby to tidy things up