Hi Derek,
It’s possible, but Contact forms are more complicated.
For instance, see this article: https://daext.com/blog/create-a-contact-form-in-wordpress-without-a-plugin/
The PHP part, you can add through Code Snippets.
The JS part, you can add through a Hook Element hooked to wp_footer.
The CSS can be added in Appearance > Customize > Additional CSS.
Then, in this sample, a shortcode can be use to make the contact form appear.
I haven’t test this code though. It’s just a sample of what it would be like to create a contact form. It would be best to research deeper to make sure that the form is secure and working.
Hope this clarifies!