I want one page of my site to be my Tumblr page and the rest of site on WordPress - all under same domain name

Hello,

So my client wants the home page of his domain burnttoastusa.com to forward to his Tumblr account.

Then he wants the rest of the site built on WordPress (about 3 other pages including a WooCommerce store)

I've built the Tumblr theme to look like the WordPress theme so that is taken care of. But I can't figure out how to make the Tumblr page the home page without messing up accessing the rest of the site.

I tried forwarding burnttoastusa.com to his Tumblr page burnttoastusa.tumblr.com which works. But when you are on his Tumblr page the links I set up that are supposed to take you to the WordPress pages once clicked don't end up going to the WordPress pages because the initial domain name burnttoastusa.com is set to forward back to Tumblr. So it's in a loop basically.

I've looked all over online for this and some people are trying to do the same thing but haven't figured it out.

I don't want a plugin to make the posts look like Tumblr posts. My client wants the actual Tumblr page connected to his WordPress site....

Any ideas?