Nope, just SQL, MySQL and Oracle are supported. Postgres is not.
I don't think you'll have a chance doing anything via ESS. FileMaker Cloud is very tight in terms of any flexibility with the application itself since you're dependent on filemaker adding the support to the core application.
That said, maybe something via Insert From URL could be done if you created your own endpoint for the PostgreSQL database to turn it into a RESTful web service instead of using ODBC.
Else, FMS on AWS is still a really good deployment option to get the full functionality of FileMaker Server. The release cycle for FMS also seems to be ahead of FileMaker Cloud in terms of features.
In what sense are you looking for a workaround?
You could change your database so it uses calls to the database via a RESTful API rather than ESS.
You could use Foreign Data Wrappers in PostgreSQL to create a connection to a MySQL "mirror" that is kept in sync via triggers.
If you're looking to make ESS work with PostgreSQL (or IBM i7.1 or IBM DB2) on FileMaker Cloud I'm afraid you're out of luck.
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