As if now, there is no direct way to tigger Lambda on the basis of such conditions. You need to write your logic in a separate lambda which will trigger your step function.
You can refer here about how to trigger a Step Function from Lambda.
Now, coming to the point about logic in your Lambda which will check for your files. Here, I believe you know all those three files or at-least you know the file prefix so when ever any file is uploaded to S3 you can check in Lambda if three files are there or not. You can trigger the state machine directly from Lambda if all three files are found else you can stop there itself. Once the Step Machines execution is complete either you can clean up those three files or you can rename it to something else or you can move those files to a different "folder" so that next time when you upload any of those three files your lambda does not triggers state machine.
The other logic I could think of is, uploading all these files together as zip. Once the zip is uploaded to S3, your lambda gets notified, processes that zip and extracts all three files, does some processing and triggers the state machine with processed data.