Unlocking features of a game

I’ve made a game where as the player completes a level the next one is unlocked (like most games), and I use this to ease the player into the increasing difficulty of the game.
For example new obstacles and/or objectives are introduced incrementally meaning in the beginning the game is very basic (get from A to B) and towards the end there are game mechanics such as collecting items and unlocking doors. This all works reasonably well.

Now I want to extend the game with four new levels that aren’t part of the “normal” sequence of levels, they’re time-trial levels that you’re supposed to play not to unlock the next one but to try to improve on your previous time.
I don’t want these levels to be exclusive to players that have finished the normal levels, but at the same time I’m worried that introducing them from the get go will make the game not only seem too difficult but also take away a bit of the “exploring” gained by incrementally giving the player new features.

How should I introduce my time-trial levels?