The Theft of the Space Stone was the attempt by the Avengers of acquiring the Tesseract from the past. After their mission in New York resulted in only the Mind Stone being retrieved, Iron Man and Captain America went back to 1970 to Camp Lehigh due to Stark knowing the Tesseract would be there as well as Howard Stark and other Pym Particles from Hank Pym, as they needed more in order to return to 2023.
The Space Stone, encased in a cube-like Tesseract, was used as the chief weapon of the Asgardians during their war against the Frost Giants. Due to different circumstances, the Tesseract came to be possessed by specific individuals and organizations such as the Red Skull, the leader of HYDRA, S.H.I.E.L.D., Tony Stark, and it was later returned to Asgard in the aftermath of the Battle of New York until Loki retrieved it during Ragnarök. However, Thanos and his forces ambushed the Statesman, thus retrieving the Space Stone, which he later used to wipe out half of the universe's population.
The Avengers, who had discovered that they could use the Quantum Realm and Tony Stark's Time-Space GPS to travel through time and space, hatched a Time Heist, in which they would travel to the past and amass the six Infinity Stones in order to undo the Snap.
Ant-Man, Iron Man, Hulk, and Captain America were tasked with going back in time to May 4, 2012, during the Battle of New York, to retrieve the Mind Stone, Space Stone, and Time Stone as half of the six Infinity Stones were in New York City on that day. Iron Man and Ant-Man were tasked with securing the Tesseract from the 2012 version of the Avengers.
Arriving to 2012, the Avengers headed to the Stark Tower, just in time to Loki's defeat. As the 2012 Avengers were apprehending Loki, STRIKE agents led by Jasper Sitwell and Brock Rumlow came to the Tower to hand the Scepter for HYDRA. While Captain America followed STRIKE agents to steal the Mind Stone, Iron Man and Ant-Man decided to steal the Space Stone. Lang quietly hid onto 2012 Stark who was transporting the Tesseract, along with STRIKE and the Avengers, while Stark departed from the building in the Iron Man Armor: Mark LXXXV and stole S.H.I.E.L.D. uniform to disguise himself.
As the Avengers reached the lobby, they were confronted by Alexander Pierce who demanded 2012 Stark and Thor to hand Loki and the Tesseract to S.H.I.E.L.D. While they were arguing, Lang caused a malfunction in Stark's Arc Reactor which caused Stark to undergo cardiac arrest. The distraction allowed Stark to secure the Tesseract. However, before Stark could exit the building, Hulk burst into the lobby from the stairwell, and causing Stark to drop the Tesseract. In the confusion, Loki managed to retrieve the Tesseract and used its power to escape.
Having failed to retrieve the Tesseract, Stark hatched an idea to recover the Tesseract as well as extra Pym Particles by traveling further back in time, deducing that in April 1970 both the Tesseract and Pym Particles were housed at Camp Lehigh in New Jersey. Heeding Scott Lang's warning that if they fail, they will be unable to return to the present, Stark and Rogers put their trust in each other and depart to 1970.
In Camp Lehigh, an incognito Tony Stark and Steve Rogers immediately deduced where the Tesseract is being held and head to retrieve it. As they were both riding an elevator, Stark, posing as a doctor, leaves on an earlier floor to retrieve the Tesseract, and Rogers, posing as a soldier, stayed on the elevator on his own mission to retrieve more Pym Particles. Stark located the Tesseract in a safe and silently broke inside it, storing it in a suitcase, but before he could leave the area he was confronted by Howard Stark who was unaware of who he is. Hiding his identity, Tony reveals his name is "Howard Potts" and he is a visitor from Massachusetts Institute of Technology.
Meanwhile, Rogers distracted Pym and lured him out of his laboratory, as he was able to successfully infiltrate and secure the Pym Particles. As Tony and Howard converse in an elevator, Rogers prepared to leave but was forced to walk in an office to hide from United States Army soldiers who were on alert from a potential breach. Upon noticing a younger picture of himself, Rogers found himself in Peggy Carter's office. He noticed her talking to another person and looked at Carter, contemplating. Leaving the base, Rogers signaled Stark that Pym Particles were secured. As their conversation closes and Howard left with Edwin Jarvis, Stark and Rogers succeeded in their missions and head back to 2023.
The Space Stone was extracted from the Tesseract and placed within the Nano Gauntlet, created by Tony Stark, Hulk and Rocket Raccoon. Following the Battle of Earth, the Space Stone was placed in a suitcase and given to Steve Rogers, who traveled back in time once again to return the stone, albeit without the Tesseract.