Is there any API or custom integration available to sync Facebook page or post like data to ingest in Marketo database?
Don't see what you're trying to do. Please provide deep details about the source in FB and the intended destination within Marketo (where in the database?).
Use case is to create Webhook flow between Marketo and Facebook business manager tool so that when any paid campaigns are run in Facebook the response based on post like, page like and other details share to Marketo. The current Marketo and Facebook native integration ingest the lead generated data from Facebook to Marketo. is there any API available to fetch and ingest the data from Facebook business Manger to Marketo? I am looking both API details i.e. Facebook as well as Marketo endpoint.
OK. None of those needs were clear from your original post! Details are always better, esp. to avoid the XY Problem.
It would be possible to build such a connector to the FB Graph API using an IPaaS platform, but no prebuilt one exists, AFAIK.