I think the notion that you are already enlightened and that there is no need to strive, comes from the Mahayana teaching of Buddha Nature or tathagatagarbha, that everyone has the natural potential to become enlightened.

This is apparently based on the sutta teaching about the luminous mind (pabhassara citta in Pali), which states that the mind is fundamentally pure, but it is defiled by incoming defilements. That's like saying, the dirty cloth, is actually pure white below all that dirt, but is soiled by dirt that got on it.

So, what you need to do is to coarsely, then thoroughly, remove the dirt from the cloth and then, prevent it from getting dirty again by ending the source of the dirt. For the mind, that's the ten fetters. The root is ignorance.

From a Theravada perspective, 'You should strive for enlightenment. Purify your mind!' is the correct way to get into the process.

If you start with 'You are already enlightened. There's no need to strive!', then you'll end up being lazy or confused. "I am enlightened, but... I am not enlightened?"

But there is a place for 'You are already enlightened. There's no need to strive!' too. In order to reach the state of jhana, the mind needs to let go of striving and simply fall effortlessly into the peace and stillness that is fundamental to the mind.

Ven. Ajahn Brahm is widely recognized as an expert of samatha meditation leading to jhana from mindfulness of breathing, with his book, "Mindfulness, Bliss and Beyond". I quote a part of this book below.

You experience every part of each in-breath and out-breath continuously for many hundred breaths in a row. That is why this stage is called full sustained attention on the breath. You cannot reach this stage through force, through holding or gripping. You can attain this degree of stillness only by letting go of everything in the entire universe except for this momentary experience of the breath happening silently. Actually “you” do not reach this stage, the mind does. The mind does the work itself. The mind recognizes this stage to be a very peaceful and pleasant place to abide, just being alone with the breath. This is where the doer, the major part of one’s ego, starts to disappear.

One finds that progress happens effortlessly at this stage of meditation. We just have to get out of the way, let go, and watch it all happen. The mind will automatically incline, if we only let it, toward this very simple, peaceful, and delicious unity of being alone with one thing, just being with the breath in each and every moment. This is the unity of mind, the unity in the moment, the unity in stillness.

The fourth stage is what I call the “springboard” of meditation, because from it one may dive into the blissful states. When we simply maintain this unity of consciousness by not interfering, the breath will begin to disappear. The breath appears to fade away as the mind focuses instead on what is at the center of the experience of breath, which is awesome peace, freedom, and bliss.

At this stage I introduce the term “beautiful breath.” Here the mind recognizes that this peaceful breath is extraordinarily beautiful. We are aware of this beautiful breath continuously, moment after moment, with no break in the chain of experience. We are aware only of the beautiful breath, without effort and for a very long time.

Now as I will explain further in the next chapter, when the breath disappears, all that is left is “the beautiful.” Disembodied beauty becomes the sole object of the mind. The mind is now taking the mind as its own object. We are no longer aware of the breath, body, thought, sound, or outside world. All that we are aware of is beauty, peace, bliss, light, or whatever our perception will later call it. We are experiencing only beauty, continuously, effortlessly, with nothing being beautiful! We have long ago let go of chatter, let go of descriptions and assessments. Here the mind is so still that it cannot say anything. One is just beginning to experience the first flowering of bliss in the mind. That bliss will develop, grow, and become very firm and strong. And then one may enter into those states of meditation called the jhanas.