Hawkman and Nabu (the being inside Dr. Fate's Helmet) were both in Ancient Egypt with Black Adam and had a "history" together. But sure, just throw them in the movie and ignore all of that and just barely explain who they are.
In the present day Black Adam joins the JSA for a while trying to prove that he is turning over a new leaf as a good guy. He strikes up a pretty good friendship with Atom-Smasher. Eventually stuff happens and Black Adam decides the JSA isn't tough enough on crime, and he decides to go on his own and he's going to start by taking over his home country of Khandaq and getting rid of the corrupt government.
He convinces Atom-Smasher to go with him, along with a few other young JSA allies. Together they take over Khandaq. Atom-Smasher is morally conflicted about killing, but Adam convinces him via showing him things like women and children in forced labour shops.
The JSA naturally find out and go into Khandaq, wanting to stop Black Adam and also t reclaim Atom-Smasher and their other young allies and try to get them back on the right path and away from Black Adam's influence.
They battle in the streets, and the people of Khandaq take Black Adam's side because he liberated them from the terrible corrupt gov't. The JSA even start to wonder what they are doing here, are they the good guys... but Hawkman tells them Black Adam has to be stopped, he's seen him unleashed in ancient times and knows what Adam wants...
Eventually the fight is only stopped by Atom-Smasher, who has been conflicted the whole time, convincing everyone to stop fighting and making Black Adam promise to just stay in Khandaq and not expand his "campaign of justice" to other countries like he was saying he would.
But in the movie, let's just replace the "legitimate" rulers of Khandaq with a literal gang of criminals who took over because that is less morally troubling than attacking a nation's army and institutions. Then let's jut ignore all the complex moral stuff with Atom-Smasher and just toss him in the movie too. Then instead of really focusing in on the relationships and the whole "nature of heroism"/"what is too much, what is too little, what can we do, what can't we do" quandaries, let's just toss in a generic demon big bad for Adam to fight and clearly just be "the hero".
Maxine Hunkle didn't exist at this point in the comics and was probably also just tossed into the movie because they wanted a female member of the team and couldn't put in Stargirl. It was good to see her, especially since she also didn't exist for like a decade until she was brought back recently.