Is there any attack move in the game?

Some of the people in the internet says it exist, but I can't find the exact specific way to do so

Sorry, there is and was no attack move in any variants of AoE 2 ever.

It's based on AoE 2 and AoE 2 didn't have an attack move, so I'd say no. They patched the attack move for the HD edtion...

You can instead use the patrol option, which acts like the attack move, however with some obvious differences.

I usually put the stance on aggressive and it works decent enough.

Jepp. Aggressive stance and always the finger on the "Stop" hotkey. When enemies attack, your troops stop marching and defend themselves. When attacking buildings, stop the current action to "free" your troops form the current task so that they can attack enemy units which might appear.

I seldom use the direct attack and let the AI do her thing. Works well in most standard situations. Only siege units with AOE attacks i put on passive stance and tell them precisely what to do.

Galactic Battlegrounds uses the AOE 2 engine,so there is no attack mode.

In fact, the Manual, when discussing the Tutorials, says if you are familiar with AOE 2 you can skip most of the tutorials, and only deal with later ones that deal with specific Content.

Mate attack move is using patrol. Press z and click and your units will shoot on sight other units.