The film begins in 1944, at Bamburgh Castle in Scotland (but as the Nazis weren't in Scotland I'm guessing it will be a castle in or near Germany).
Jurgen Voller (Mikkelsen) and Thomas Kretchmann's character (Colonel Weber) open a box, perhaps containing a piece of the Antikythera quadrant: a circular machine built by Archimedes in Syracuse in the 3rd century BC (a calendar or calculator).
Indy is captured and interrogated in the same room.
Basil Shaw (Toby Jones) is a friend of Indy and he helps his friend causing an explosion in the castle (or the Allies attacks the castle).
Indy frees himself while he’s being taken away and steals the Antikythera.
The escape by motorcycle and sidecar takes place together with Basil and they take the Nazi train.
Indy recovers his clothes while still dressed as a Nazi (so it was either premeditated that they boarded the train at the end of the mission or Basil in the Sidecar had the bag with all Indy's effects).
Indy and Basil faces Colonel Weber on the train and some soldier, then they jump off the train with the Antikythera.
They go to Oxford, to Basil’s house, according to leaks on the set there is a little girl at the window (it is little Helena, daughter or granddaughter of Basil played by Imogen Inman).
It seems Indy and Basil will have a fight because Indy breaks into his friend’s office.

1969, Indy is in New York, still teaches archeology (the one projected on the wall is a Phoenician archaeological artifact, with Minoan artifacts from 1400-1100 BC on the desk).
Indy goes to Egypt to meet Sallah (there is a Cairo taxi) who leaves him at the airport and gives him good luck for his last day as a teacher, Voller observes everything from the distance.

Helena "sneaks" into the archive that Indy frequents in New York (to recover the artifact found by Indy and her Father in 1944.
New York City Parade for Apollo 11, August 13 1969, while there’s a Vietnam War Protest.
Indy has something with him, some kind of watch similar to a gift, an awards for the end of his career.
However the basis is similar to the Antikythera device in the hands of Basil in the leaks but I don’t think it’s connected to it.
Indy faces Shaunette Renee Wilson (CIA agent named Mason), Klaber (Boyd Holbroook) and his mens, who want the Antikythera stolen from the Nazis in 1944.
The fight starts while Helena watches everything from a roof and Voller spyes Indy.
Indy steals a horse and faces Klaber on a motorcycle, then escapes in the subway.
Indy and Helena finally meets and she asks for help since she is her goddaughter And the enemies were Nazi.
Indy accepts and takes the piece of the Antikythera, the couple goes to Morocco to deal with a gangster who possesses another piece.
The two meet a boy who can guide them through the streets of Morocco, maybe his name is Jamie according to the Leaks.
Indy and Helena meet with the gangster but the negotiations fails (especially when Voller, Klaber and Klaber's giant henchman is the one who interferes).
Indy steals the piece of Antikythera on the table by putting it in his purse and threatens everyone with the whip before fleeing with Helena.
The chase takes place through the streets, Helena confronts Voller by getting into his car.
Here her red dress is torn off, from here on she will only wear the white dress.

The trio thus goes to the Temple of Segesta to follow the clues left by the Romans or the Greeks who had to do with the Dial Of Destiny (the complete Antikythera).
Jamie (or Helena or both) is kidnapped in a blue van and Indy races to his rescue in a wedding car.
We then move to Marsala, Sicily, and meet the character of Antonio Banderas.
His character appears to be an old friend of Indy's and is the captain of a boat (or a small fishing boat).
Banderas, Indy and Helena head to a point in the sea where a Roman or Greek boat should have sunk (ended up in a crevasse).
The three put on their Scuba suits and dive down to find the wreck, which contains a skeleton and a chest with possibly another piece of the Dial or some other clue.
They find the chest, tie it up, and send it to the surface with some sort of flare.
The next sequence is set in Syracuse, with Indy and Helena underground walking across a bridge.
I deduce they are in Syracuse because the writing on the walls is Greek and there is a statue of Athena.
The two explorers find a statue of Atlas holding up the world and use a lever to flip the globe.
As Archimedes said: "Give me a lever and I will lift the world."
As the globe flips over the mechanism is activated and Indy and Helena find a tomb with the final piece of Antikythera inside.
As they are about to leave Voller's giant henchman attacks them as a trap is sprung.
The three fall into a water trap but Indy and Helena manage to save themselves and block the henchman underwater with handcuffs (perhaps taken from Mason's character who followed them from New York).
While Indy, Helena and Mason go to a private airport to leave for the United States Indy is attacked by Voller and his men dressed as Nazis, ready to take possession of the Dial and make the time travel to World War 2 and create a new timeline where Nazi won the war.
Indeed, Antikythera marks the coordinates for a space-time rift that will allow an air vehicle to navigate through time.
So Voller and the Nazis steal the Dial and drag Indy into a WWII airplane.
Helena tries to reach the plane with a motorcycle and manages to get on board while Mason and Jamie follows them with another plane.
Unfortunately, the plane reaches the rift and enters it.
Indy and Helena parachute and land on a prairie in Syracuse as the plane crashes.
Here the two discover that they ended up in Syracuse in 212 BC, during the Siege of Syracuse (clash between the Romans and the Greeks).
According to history, the Romans killed Archimedes in his laboratory in this historical period, in fact it seems that some shots were taken at the castle of Maniace (in Sicily) to create the interior of Archimedes' laboratory.
My investigation ends with the photo of the Siege of Syracuse with the presence of a plane wreck (the crashed Nazi plane with Voller inside) and an airplane landed near the houses (perhaps Mason and Jamie's plane which followed them into the space-time rift).