Submit Typeform by click on the custom button

We are trying to implement TypeForms in our React website. But we do not like the standard design of forms, it does not match the overall style of the website. So we decided to hide the form and put the values from our custom form fields to the hidden fields of the TypeForm (we already found how to do this via hidden fields). The only thing we haven't figured out yet is how to submit TypeForm when we click our custom button. Is there any way to do that?

Or perhaps there is an easier way to pass data from our forms to TypeForm?

Any help would be helpful as we want to use TypeForm everywhere in our many applications, but we definitely need the ability to style them. Thank you!