On a website, is it possible to fill in fields of a form on another domain that doesn't use query string parameters?

I have a website that links to a donation form on another domain's website. Is there any possible way to fill in some of the fields of that form when the page loads on the other domain? (The other domain's website doesn't use query string parameters.)

I'm open to any suggestions using any kind of web frameworks and technologies to try to hack this together. E.g. loading the donation website's form in an iframe, or cookie manipulation (though I'm pretty sure there's no path of success here since security features prevent anything applicable), or recreating the form on my website and targeting the same submission action that's on the donation website's form.