Officers said there was now a "deep understanding" of Abedi's movements in the weeks leading up to the attack.
The head of counter terrorism said it was "less clear" whether he had obtained and stored all the materials or if others were "complicit".
All 22 people arrested over the attack have been released without charge.
Det Ch Supt Russ Jackson said Greater Manchester Police now had details of Abedi's movements in the weeks leading up to the Manchester Arena bombing.
These included how the chemicals to build the bomb were obtained and where he put the device together.
Police said they had an understanding of Abedi's movements "almost hour by hour" in the days before he bombed Manchester Arena on 22 May.
They said:
Early in the investigation, GMP said it could be looking for a "network" of people in connection with the attack, but all of those arrested so far have now been released.
Two were quickly de-arrested, but the other 20 were interviewed multiple times about their contact with Abedi.
Det Ch Supt Jackson said they had uncovered "a number of suspicious purchases" of materials, which could be used to make bombs, as well as contact with the attacker.
Some of those arrested gave accounts of "innocent contact" with Abedi and police were "satisfied with these explanations".
He added: "We said at the start we had to rapidly understand whether this was an attack committed by an isolated individual or a wider network.
"We have made enormous progress in this and are far more confident on who was not involved and who could still be involved."
Officers are continuing to search a landfill site in Bury, Greater Manchester, for a blue suitcase that Abedi was seen using days before the attack - it is believed to contain items discarded after the bomb device was assembled.
They said they had "found evidence of explosive material at several locations" after searching 29 premises that had links to Abedi.
Police also want to talk to Abedi's younger brother, Hashem, who left the country on the same day as his brother and is being detained in Libya.
Assistant Commissioner Mark Rowley said the pace of the inquiry, which is one of GMP's largest investigations, was "incredible and will continue in the coming weeks and months".
More than a thousand officers have been working on the investigation, which has seen the seizure of about 700 media devices, including phones, and more than 8,000 entries on the police's logging system.
Det Ch Supt Jackson appealed again for anyone who may have seen Abedi in the days before the attack to come forward - especially those who saw him with the car or putting materials into it.
"This is very much a live criminal investigation moving at considerable speed," he added. "It is a terrorism investigation relating to 22 murders and multiple attempted murders.
"It will continue at its current pace as we work to understand the full extent of the involvement of anyone else."
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Manchester bomber Salman Abedi was likely to have built the device that killed 22 people alone at his flat, police have said.