Filemaker can't access the DOM tree as an object in the web viewer. The best it can do is pass parameters with the URL.
If the page is your own and you can write the code then I'd use jQuery to submit the form on document ready if the parameters / conditions are met.
If you only want to submit some data, you might even consider writing your own API on the website for this purpose. Then you can use "Insert from URL" script step to look for the response that confirms the action was OK.