Enter name and email on the Product page and keep the input data on the Checkout page

I developed a custom Product page where I have to place the form with the Name field and Email address field. When I click a Purchase button Woocommerce links me to the Checkout Page (I avoided the Cart page). How can enter name and email on the Product page and keep the input data on the Checkout page? I broke my head trying to find an appropriate solution, but unfortunately can't get how I can do that. Much appreciate any help!