I considered this question for people with disabilities (i.e. blind people) who don't have Javascript.
An ugly solution would be to call ReCaptcha from the server, get the prepared HTML, submit it to the browser, submit the form when the user clicks, and then send the user input from your server using Javascript.
It seems that Google in any case explicitly prohibits calling its ReCaptcha APIs from the web server. This means that using ReCaptcha without Javascript is not possible.
For iframe, I have not tested.
In addition, you need to understand that Google and other software vendors like to provide the javascript SDK because it is easier to maintain. If you hacked internal JS / iframes to directly call the API, probably after a few months the JS changed and your hacked file was broken ...
However , you can use ReCaptcha without JS: How to hide recaptcha for JavaScript-enabled browsers and pass html confirmation
Basically following the link provided and using the example user968834
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