The moon landing happened in 1969, not 1963, so this is definitly another earth. Which leaves two possibilities:
1) alternate superman travels to our earth and creates the team, then something happens to him, and the main one is like "so... wanna go punch an interplanetary slaver?""eh sure why not".
2) the rest of the team is from an alternate earth, which means dont get attached to this apollo, midnighter, black, enchantress and natasha because they're either getting killed or going to limbo when this is over.