There is a confusion here. GoDaddy offer several services and you have two of them mixed up:
- DNS.
- HTTP redirects.
With DNS, when you point a domain (or subdomain) at an IP address, a client types that domain into their browser, the browser looks up the IP address and sends the request to that IP address (your web server).
With HTTP redirects (which GoDaddy calls Forwarding), the client types in the domain and the IP address they get back is GoDaddy's web server's IP address. They send the request to that IP address and that web server responds with a 302 redirect response that tells the client to make a new request to your IP address.
Due to ambiguity/misinterpretation with the original HTTP RFC, the follow up request is always a GET request, even if the original was a POST request. To remove this ambiguity, newer HTTP RFCs have added the 303 and 307 redirect codes. I don't know if GoDaddy offers these codes as choices when forwarding.
To solve your problem, don't use Forwarding. Go to the Zone editor in the GoDaddy web interface and point your subdomain directly at your IP address. (If "Google Cloud" requires a CNAME entry pointing at a domain they control, you can do that in the Zone Editor too.)