I found 2 different ways:
First one: Just write a simple NodeJS App Engine Service (or java or python as Document AI currently offers client libraries for these 3 languages) that acts as a proxy between the .netcore service and the Document AI api.
Second One: Create an Api Key in the CGP project and grab it as an environment variable in the .netcore service. Then, just send and http post to the url adding the api key as a query param like:
https://eu-documentai.googleapis.com/v1beta2/projects/{YOUR_PROJECT_ID}/locations/eu/documents:process?key={API_KEY}
And that's it.
About the second one, I'd prefer not having to use an ApiKey. I'd like to know how client libraries such as nodejs's manage to send the request to DocumentAI api without the ApiKey. In my first attempt, I expected that using the HttpClient from GCP Service Account Credential would do the trick, but I got a 403 error pointing that an api key was missing. What I did was:
var cred = GoogleCredential.GetApplicationDefault()
var credential = cred.UnderlyingCredential as ServiceAccountCredential;
var uri = new Uri($"https://eu-documentai.googleapis.com/v1beta2/projects/{YOUR_PROJECT_ID}/locations/eu/documents:process;
var responseMessage = await credential.HttpClient.PostAsJsonAsync(uri, config);
var response = await responseMessage.Content.ReadAsStringAsync();
As already said, this produces a 403 error complaining about missing an ApiKey. When using the ApiKey you can use a regular HttpClient, using the HttpClient created for the Google Credential is not required