However, this comic took place right after the medal ceremony at the end of A New Hope. If the destruction of Alderaan just happened, how was the statue built so quickly?
The simplest answer is that although a relatively short amount of time passed between the destruction of Alderaan and the Battle of Yavin (approx 2 days, depending on how long it took for the Death Star to follow Leia), it was a sufficiently long period to have allowed news to have reached the troops prior to their arrival. This presumably would also have allowed some budding artiste to have time to chuck up a statue.
“Commander Willard!” Leia threw her arms around him. The man looked momentarily overcome with emotion.
“When we heard about Alderaan, we were afraid that you were…lost, along with your father,” he said. “How are you holding up?”
There's also the possibility that the statue pre-dates the couple's death. They were prominent figures in the Resistance and certainly worthy of admiration.