AWS Step Functions - is there such a solution for Google Cloud Platform?
Cloud Workflows was announced at Cloud Next On Air 2020.
2021 Update
As Brian de Alwis noted below, since this answer was written Cloud Workflows is now generally available and is functionally similar to Step Functions.
2019 Answer
As far as I'm aware there's nothing specifically like Step Functions, but I have two strategies for creating these types of micro-service systems on Google Cloud.
Strategy 1: Cloud Run/Cloud Functions with Pub/Sub
Here I'd create microservices using Cloud Run or Cloud Functions and subscribe these functions to Pub/Sub topics. That means that when Function A executes and completes it's work, it publishes a message to a specific topic with a data packet that any function subscribed to it will receive and execute.
For example you could create two topics named FunctionASuccess and FunctionAError and create two separate functions that subscribe to one or the other and handle the success and error use cases.
Strategy 2: Firebase Functions with Firestore/Realtime Database
Similarly to above I create Firebase Functions that watch for changes in Firestore or in the RTDB.
So Function A executes and completes its task, it saves a document to the FunctionAResults collection in Firestore or RTDB. Functions that are subscribed to changes in the FunctionAResults collection are then executed and take it to the next step.
They both work reliably so I have no preference, but I typically go with the 2nd strategy if I'm utilizing other Firebase services.