Start by thinking of it in terms of Euler rotations. Using Ampere's hand / right-hand rule, "start" with your hand aligned with the "origin" ECI frame. Imagine that your right-hand is centered on the Earth, so a spacecraft will be in orbit around your hand. Specifically, its furthest distance from the origin is the semi-major axis, but since we're in a circular orbit, the spacecraft's only distance is the sma. We'll work through finding the correct "destination" frame. You know that you've "reached" the destination frame when the motion of the spacecraft can be represented by a rotation around a single axis. Looking at the right-hand rule diagram below, it means that the motion of your spacecraft corresponds only to a rotation around your thumb.
Think of the right ascension of the ascending node. What does it mean in terms of geometry? It means that spacecraft will always cross the orbital plane at that angle compared to the "origin" of the frame. Looking at the right-hand rule diagram below, that orbital plane is the plane created from the vectors a and b. The RAAN is measured from the origin frame, therefore from the a vector. Therefore, in terms of rotation, the RAAN corresponds to a rotation about the a-cross-b vector (i.e. your thumb). That corresponds to an Euler rotation by the 3rd axis.
Now, imagine what it means for your orbit to have an inclination with respect to your right-hand. It corresponds to a rotation about your index finger, which is the 1st axis. So far, we've done two rotations: by the 3rd and the 1st axis.
The final rotation will be for the true anomaly of your orbit. As discussed in the first paragraph, at this point, the motion of your spacecraft is fully described by a rotation of your thumb, i.e. a rotation around the 3rd axis. This means that, after we've accounted for that rotation, we'll have done a 3-1-3 Euler rotation, where the angles are respectively the RAAN, inclination, and true anomaly.
So what's the starting vector which you need to multiply your direct cosine matrix with? Well, back-tracking to the start of the problem, we've stated that the spacecraft was described as rotating around your hand, and we've done all of the rotations with {index, middle finger, thumb} as the frame. Therefore, the initial vector is [sma; 0; 0].
Further, in a circular orbit, the angular rate is constant. Therefore, you can compute the orbital period from the mean motion and the GM of the Earth: the period is simply 2-pi divided by the mean motion. Finally, you know how long it has been since the spacecraft periapsis passage, so you can fully determine the true anomaly.
You now have all of the bits to create the X, Y, Z state from the data you were given. Let me know if this explanation needs clarification.
