Hi Carolyn,
Google does have an API specifically for GMB and it is one of the few Google APIs for which you must apply to gain access:
Google My Business API: Application Form For Basic Access
Before you can apply, you need to have or create a Google Cloud Platform (GCP) "project" to which you'll provision GMB API access. GCP projects are used for metering, billing, etc.:
Google Cloud Platform
Then it's a matter of your devs navigating Google's GMB API docs for the actions they want to perform, e.g. creating posts:
Create Posts on Google | Google My Business API | Google Developers
Note that API changes are afoot so anything your team builds will require some maintenance over time. Google provides API client libraries in different programming languages which may or may not ease the burden:
https://developers.google.com/my-business/samples
Hope this helps. Building something to handle a discrete action like creating posts shouldn't be a huge dev effort and shouldn't require prior familiarity with Google's APIs. And in the end, you'll own the tech, which is nice