A different outcome is if the Confederates won instead.
If the Army of the Potomac suffered a defeat in detail early in the war, there would have been little to prevent Lee and Jackson from investing Washington and dictating terms. Lincoln probably would have negotiated peace and retired in disgrace in 1865.
A quick victory was less and less likely after Antietam, since the greater manpower of the Union was already in play, and their ability to produce weapons and naval vessels was obviously greater.
By the time of Gettysburg, Lincoln had already issued the emancipation proclamation and polarized the two sides in ways that were not possible before. Secondarily, the loss at Vicksburg and the ongoing defeats of the Confederate Army of Tennessee made the west a costly secondary front that the Confederacy couldn't afford.
Even with a Confederate win at Gettysburg, they would have had to completely ruin the Army of the Potomac and hope that they could invest Washington before troops could be brought up from the west. The entire campaign was a massive gamble, but given Lee's early successes, it was a calculated risk that he thought was worth taking.
Given the early issues that the Union had with leadership, I don't believe their victory was always assured, but after depleting the Confederate ranks and winning a few battles, a Confederate win became less likely over time.
It was significant because it stopped Confederate General Robert E. Lee's second invasion of the north.