There were many incarnations of Indiana Jones's journeys, and the game that Indy and Sophia were featured in, "Indiana Jones and the Fate of Atlantis", was one of them.  All of the Indy movies, shows, books, and games all go together, because they star Indiana Jones, but were as a whole pretty individual.  However, there was always a chance that all of these things worked together to form one true Indiana Jones story.  Regardless, I am only going to talk about Indy's past specifically mentioned in this game, and not go into the movies or anything else that may not be true for this story.

In this game, Indiana Jones was the same old lovable, adventurous, ambitious archaeologist that you have probably seen in the movies.  Indy started the game looking for his old friend Sophia Hapgood, who had accompanied him on an archaeological dig in Iceland many years earlier.  As he looked at a National Archaeology magazine that featured the two of them, he noted that the article was written back when he thought they might like each other.  Indy also noted that she stole some Atlantian artifacts from the expedition to further her own career as a psychic.  He met up with Sophia again in New York where she was giving a presentation on her theories of Atlantis.  She left the show in the middle because Indy interrupted it and left with him to talk.

It was always a dream of Sophia's to find Atlantis; she even had a spirit that guided her thoughts who was a king in Atlantis, Nur-Ab-Sal.  Indy picked on her throughout the game because he thought she was faking it.  She revealed to him her most prized possession, her necklace, which was an Atlantian artifact.  Sophia also shared with him the secrets of the orichalcum beads, which she believed the Nazis were also looking for, in addition to Atlantis.  Indy and Sophia decided to team up and find "The Lost Dialogue of Plato", which they believed held the secrets to finding Atlantis.  The traveled to many different places and eventually found it right in Barnett College, where Indy was a professor.  The duo headed back to his office to decide what they should do from there, now that they had the Lost Dialogue, a key factor in finding Atlantis.  Sophia told his fortune before they headed any further, and Indy had a choice of whether or not to continue the rest of the mission alone.  Although the player had a choice at this point of which path to take, the best one, in my opinion, was the one where Sophia accompanied Indy.

Regardless of whether or not they make the journey together, Sophia was eventually taken prisoner by the Nazis, along with the three stones Indy had collected to gain entry into Atlantis.  He stowed away on their U-Boat and rescued her, retrieved the stones, and guided the U-Boat into the underwater entrance to Atlantis.  Sophia was then taken by Kerner, the Nazi leading the expedition to Atlantis, and Indy once again has the option of what to do.  He either rescued her and took her with him or left her in the cell he found her in.  As Indy and Sophia headed closer to the central room of Atlantis, she became completely possessed by her spirit guide, Nur-Ab-Sal, and Indy realized she has indeed been telling the truth the whole time.  He made her give up her necklace which Nur-Ab-Sal was using to take her over, and threw it in the lava pit.

Indy and Sophia eventually made it to the "God Machine" where they ran into the Nazis.  Kerner wanted to become a god using the orichalcum they found, and Sophia and Indy watched as the experiment failed and he fell to his death into the lava.  The scientist Ubermann then tried to get Indy to go next, in case they incorrectly guessed the number of beads again.  Indy eventually convinced Ubermann to go instead, which resulted in his death as well.  As Atlantis began to sink, Indy and Sophia narrowly escaped onto the U-Boat.  As they watched their discovery disappear below the waves, they shared a kiss and watched the sun set together.  If he didn't save Sophia from the cell, Nur-Ab-Sal took her over completely and she died in the room with the God Machine, so the way to get the "good" ending was to save her.

Since Indiana Jones had many incarnations, and Sophia was only in one of them, it is easy to picture them together in at least one.  Each version of Indy is different, like an "alternate universe" type thing.  Out of all the women in other Indy stories, we thought Sophia was the best and they made such a cute couple.  I can see Sophia and Indy teaming up on future adventures, since they made such a good team in this game.  As long as Indy didn't leave her to die in the game, they could have quite a happy future together!  I think that they were both in the latest Indy games "The Infernal Machine" and "The Emperor's Tomb", but since I've never played them I am not entirely sure what goes on between them, if anything.

This scene took place after Indy rescued Sophia from the cell in Atlantis.  The Nazis had kidnapped her and Indy took quite some time to rescue her because he had so much else to do first.

Sophia: "You know, I outta slug you!"

Indy: "Come on Sophia, don't be angry."

Sophia: "Angry!?  You left me rotting in this hell hole!"

Indy: "Well, if that's the way you feel, maybe you should stay in here!"

Sophia: "Maybe I will!"

Indy: "Great idea!"

Sophia: "Fine."

Indy: "Fine."  [they kiss]

Sophia: "What was that?"

Indy: "I'm not sure, I think Nur-Ab-Sal made me do it."

Sophia: "Is that so?" 

[they kiss again] "Dangerous fellow, that Mr. Sal."

Indy: "Yeah, well, we better be going..."