Entropy is not disorder. Entropy is a measure on how good a given system can dissipate heat. You can measure entropy based on this.
Proteins for instance are a system highly ordered and entropic.
You don't see entropy, you measure entropy, macroscopically as heat dissipation, microscopically as a function of all states accessible at a given temperature.
The universe is going to the direction of maximum possible dissipation of heat, like pool balls slowing down on the pool table after a hit. We are too small and live too little to really see this in practice with our eyes.
To see entropy in action, just look at the mirror, you are alive thanks to entropy. If you remove heat and entropy, your atoms would be frozen and you wouldn't exist as a human being in the first place
That's not true. A living creature exists because entropy has increased overall in each process of its existence. Every biological process that happens in your body results in an increase in entropy, otherwise it wouldn't happen.