Now that I've posted by new classes for Golden Age Supers OSE, I thought I'd briefly discuss how the core classes fit into the setting (and what changes I'd make).
In the golden age settings clerics can be archeologists granted powers by a divine artifact they find, the decedents of a god, or even a partially depowered deity themselves.
Fighters are largely unchanged. They are proficient with all modern and archaic weapons and armor, including explosives.
Magic-Users are largely unchanged. Either through research or luck they've discovered arcane secrets. Unlike their earlier predecessors, modern magic-users have learned to use some modern firearms for the protection. While most disdain them, magic-users are proficient in the use of pistols.
Whether classic criminals, spies, or those that hunt the former down, thieves are still a common class in golden age supers settings. While they aren't silent, modern thieves have embraced the use of firearms and explosives and some even uses rifles and train as assassins. Instead of a thief den they will establish a hideout or safe house.
While the demihuman classes aren't in the free basic rules pdf, I would say you can add them to the game as is. I would initially limit them to only archaic weaponry, though after reaching level 2 you may want to allow them to use more modern armor and weapons. Give them the class feature below. While initially out of place, these character could be like the League of the Realms from Marvel's War of the Realms event.