The man -- ID'd in the lawsuit as Robert Leahey -- says the incident happened back on Dec. 8, 2022 during the Rams vs. Raiders "Thursday Night Football" game ... when he was hired by Contemporary Services Corporation to help assist people in large crowds and help "maintain an orderly atmosphere."

At around 6:30 PM inside the Inglewood stadium, however, Leahey says a "large fight broke out" between L.A. and Vegas supporters -- and he jumped in to try to keep the peace.

But, in the lawsuit, Leahey says as other guards arrived on scene -- they pushed him, causing him to fall down a set of concrete stairs.

Leahey claims he hit his head several times while crashing down the stairs -- and when he got up, he alleges someone involved in the fight threw a Modelo beer can that connected with his head ... 'causing him further injury.

Leahey says on Dec. 9, he went to a nearby hospital ... "where he was tested and diagnosed with severe and catastrophic brain injuries, including a subdural hematoma with brain bleeding."

In the suit, Leahey claims since the incident, he's had difficulty with his speech and his vision -- while also suffering from headaches. He claims he's been unable to work as well.