The context isn’t really right for creating a new post. You’ll be on single-product.php if you’re viewing an existing post, but not for a post that you’ve yet to create!
I can think of two approaches.
1 – put an “Add Product” link or button onto your existing form and configure it so that a new product is created and you are redirected to that product so that you can now fill in your existing edit form to complete the data entry. I guess this kind of mirrors what the WP Admin does.
2 – just have a page template (or custom template with a custom URL rewrite) with the New Product form on, replicating pretty much what you already have in your edit form.
Hard to give some helpful code with no code in your question but hopefully these pointers will help.
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