There is an alternative, but please do install this add-on! Rated 5 out of 5 stars
I tested this add-on thoroughly for two days (48hrs). It worked flawlessly.
There is an alternative to open the new tab page: the plus-sign on the right side of your tab bar. But don't let that stop you from installing this add-on. Highly recommended!
What you're describing is essentially the built-in button for opening a new tab that's already included in Firefox. When customizing you can actually drag it to the nav-bar, but then you will no longer have it in the tabs bar next to the latest tab.
But what if you want to have it in both places? :)
Basically this is what this add-on enables you to do!