Calling Dialogflow from a website and getting a text response

I'm trying to make a webpage that has microphone input, records and sends that audio to be transcribed by Dialogflow, and then receives the text back to use on the webpage. For example, you say "rainbow" in the mic, and with the help of Dialogflow decoding, you see the text 'rainbow' on the screen.

I have a Dialogflow agent (that doesn't even have any intents, because the AI doesn't have anything to do beside simply transcribe the audio as it was spoken), but I don't know how to have it send/receive external requests. I'm new to all of this and am very lost.

I have read about Node.js, Google cloud SDKs, and various other apps like Kommunicate but I'm still not clear on how to use them or what they are even for. I can't find anyone else doing the same application as me. I don't want just the embedded Dialogflow module using their HTML iframe, I want data I/O from Dialogflow with no UI.

Some people say it's possible, and some say it's not. It seems like it should be a clear solution. There should be some sort of call function from my webpage that sends a .wav file or whatever, and then a receive function that gets plaintext. Going crazy, please help!