I'm not aware of any way to get the built-in new tab page to stop looking at your history without filling up all the tiles yourself.

What do you think about modifying the page settings to only show the number of tiles you want to see? Here's where you would do that:

(1) In a new tab, type or paste about:config in the address bar and press Enter. Click the button promising to be careful.

(2) In the search box above the list, type or paste newt and pause while the list is filtered

(3) Double-click the browser.newtabpage.rows preference and change it from 3 to 1.

(4) If needed, double-click the browser.newtabpage.columns preference to modify it back to 3 if it was changed to some other value.

That should give you just one row of three thumbnails.

Hopefully someone else has a less hackish workaround, but I think that should do it for now.

I did that before making this question, but it just makes the irregularly stretched out.

You can pin about:blank pages to tiles that you do not want to use. You probably need to create a about:blank bookmark and drag this bookmark to each of the tiles.

I tried but it only allowed one tab, unless I did something wrong. Here's what I did, typed "about:blank" in url bar, clicked and dragged that tab to my bookmarks toolbar, from the bookmarks toolbar drug the about:blank bookmark to tabs page. From there trying to add anymore would just move the one single tile around.

EDIT - Found a workaround, I'd edited the bookmark url by adding numbers, ex. about:blank1, about:blank2. That works but will make the page fail to load (but who would click it anyway)

You can use these with a ?# appended:

about:blank?1
about:blank?2
about:blank?3
about:blank?4
about:blank?5
about:blank?6
about:blank?7
about:blank?8
about:blank?9

Your first suggestion worked, I just wish there was an official way.

Here's what I did:

(1) enter about:config in the url bar and press Enter. Click the button promising to be careful.

(2) In the search bar above the list, type newt and press Enter.

(3) Change browser.newtabpage.rows to 0.

(4) Change browser.newtabpage.columns to 0.

(5) Change browser.newtabpage.storageVersion to 0.

So far it's working.