Your broad intuition is right, conformational changes–like the flipping of a cyclohexane ring–happen because of combinations of vibrations and rotations in the molecule.

But it helps to put this in context. Even at room temperature there is a lot of thermal energy available to drive vibrations and rotations in many molecules. And that thermal energy is well distributed across many of those modes (and molecular motion of the whole molecule, molecules banging into each other is happening very fast and redistributes vibrational and rotational energy).

Flipping a cyclohexane ring (swapping equatorial for axial hydrogens or other substituents) requires coordinated changes across all the bonds in the molecule. (Remember, If the ring were "frozen" in the chair conformation, there would be two distinct types of hydrogen in a cyclohexane but at room temperature we see only one which implies the chairs flip rapidly). The lowest energy conformation is the "chair". But other conformations (eg the "boat") are also seen but have higher energy. But there is enough thermal energy at room temperature to drive the specific series of vibrations and rotations that convert chair to boat and to the opposite chair conformation.

The activation energy barrier to the flip is ~40kJ/mol which is small enough to overcome from normal thermal energy at room temperature. But it isn't just a single vibration or rotation that achieves this, it is a combination of many. Since the thermal energy is well distributed the sequence of vibrations and rotations is readily explored quickly at room temperature.

Many other molecules also have enough thermal energy to cause vibrations and rotations to change their conformations at room temperature.

Your broad intuition is right, conformational changes–like the flipping of a cyclohexane ring–happen because of combinations of vibrations and rotations in the molecule.

But it helps to put this in context. Even at room temperature there is a lot of thermal energy available to drive vibrations and rotations in many molecules. And that thermal energy is well distributed across many of those modes (and molecular motion of the whole molecule, molecules banging into each other is happening very fast and redistributes vibrational and rotational energy).

Flipping a cyclohexane ring (swapping equatorial for axial hydrogens or other substituents) requires coordinated changes across all the bonds in the molecule. (Remember, If the ring were "frozen" in the chair conformation, there would be two distinct types of hydrogen in a cyclohexane but at room temperature we see only one which implies the chairs flip rapidly). The lowest energy conformation is the "chair". But other conformations (eg the "boat") are also seen but have higher energy. But there is enough thermal energy at room temperature to drive the specific series of vibrations and rotations that convert chair to boat and to the opposite chair conformation.

The activation energy barrier to the flip is ~40kJ/mol which is small enough to overcome from normal thermal energy at room temperature. But it isn't just a single vibration or rotation that achieves this, it is a combination of many. Since the thermal energy is well distributed the sequence of vibrations and rotations is readily explored quickly at room temperature.

It is also worth noting that your claim that "translational and rotational motion do not change the intrinsic coordinates of a molecule and won't bring about a conformational change" is clearly not true for the cyclohexane example. The combination of bond rotations do change the spatial relationships of the atoms in the molecule. The major rotations around the C-C bonds, for example, swap the orientation of the hydrogens attached to the carbons.

Many other molecules also have enough thermal energy to cause vibrations and rotations to change their conformations at room temperature.