Google Cloud platform gives different options to transfer files to your instance back and forth. You can check this [documentation] (https://cloud.google.com/compute/docs/instances/transfer-files ) to find more options.
You can use a third party tool to connect to any instance that is configured with the matching public SSH key file. You have to configure the public key on the server side. In this [link] (https://www.youtube.com/watch?v=wDcjM7BySo0 ) you can find a video that gives you step by step procedure to set up cloud FTP with FileZilla.
You can use SCP to transfer your files securely and the scp tool uses the same key files that you use to connect to your instances using standard SSH.
As you said in your initial post that you were able to setup FTP and transfer files between GCE VMs. In order to connect to your laptop you need to make sure you setup the FTP server properly and is listening in your VM instance. In the firewall rule of your GCE network you need to open port 21.
If you have any more questions and concerns you can follow this [video] (https://www.youtube.com/watch?v=wDcjM7BySo0) and follow the step by step procedure to establish FTP connection.--
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