Import Full Site Editing templates

Your .zip should be a fully functional theme, not just the templates. You could use the TT1 Blocks theme as a starting point, replacing its templates with your own. Rename the theme of course, including the header comments in style.css.

To install your theme, go to the themes admin screen. Click “Add New”. On the next screen, click “Upload Theme”. Choose your .zip file in the next dialog, then click “Install Now”.

If you’d rather not duplicate all the theme code, you could create a child theme instead, specifying TT1 Blocks as the parent. Any templates named the same as the parent’s will override the parent version. You then of course would also need the TT1 Blocks theme installed on the site along with your child theme.