Hannah Gutierrez-Reed's manslaughter trial kicked off Thursday, and both the prosecution and defense have revealed their hands for the court battle ... with the prosecution laying the blame squarely on HGR while the defense is pointing to a broader institutional failure.

The "Rust" armorer -- who was charged with involuntary manslaughter in the death of cinematographer Halyna Hutchins -- appeared in a New Mexico court, and the opening statements took place not long ago.

The prosecution started the whole trial by first saying they believe it was Gutierrez-Reed's fault the live round that killed Hutchins ended up on set in the first place.

Prosecutors say Hannah didn't always adhere to safety protocols on set ... for example, they claim she didn't offer to show the actors the rounds inside the weapon or have the gun inspected in front of them -- a protocol prosecutors insist she was supposed to follow.

Hannah not following protocols was common on set according to the prosecution, which claims they'll provide several witnesses who will testify about Gutierrez-Reed not adequately performing her duties.

They say she regularly left guns and ammo just lying around the set ... and even allowed live ammo to make its way on set. They even claim Hannah couldn't recognize a live round when it was sitting in her lap.

In Hannah's defense, her lawyers say she was tasked with multiple jobs on set when she was just 24 -- both armorer and prop assistant -- which was a lot to ask her to do. Her team claims Hannah's age and relative anonymity make her an ideal scapegoat for the tragedy.

And, they're also saying she did her job well ... noting she even asked the production manager for more armorer days -- because she was splitting time between jobs and wanted to focus on her responsibilities in that domain. Her lawyers say her request was ultimately denied by the production.

In addition, the defense says OSHA -- a government agency in charge of health and safety for workplaces -- found numerous mistakes in the production overall that can't just be pinned on Reed individually. The defense added OSHA fined the production ... a fine they say was one of the largest in New Mexico's history.

Alec Baldwin was also mentioned ... with Hannah's layers saying he violated the most basic gun safety rule -- don't point a gun at someone unless you want to shoot them. They say he either had his finger on the trigger or pulled it ... but either way, it wasn't Hannah's fault.

The trial's supposed to run through March 8 ... filled with what we imagine will be a ton of twists and turns.