The defeat of Lord Voldemort by Harry Potter was a turning of the tide. As Hagrid stumbled out of the wreckage that was James and Lily Potter's home, he knew without a shadow of doubt that the world would never be the same. Cradling young Harry in his arms, he could feel the weight of the new world on his shoulders. As Hagrid got onto Sirius' motorbike and took off into the air, he could not help but wonder what the new wizarding world would look like and what would become of young Harry Potter, the Boy Who Lived.
Hagrid's concern was well-founded. Whilst the inhabitants of the Wizarding World were out there, celebrating Voldemort's "death," the Muggle world was left bewildered and terrified by strange occurrences around the globe. Whilst Mr. Dursley only had to contend with grown men running around in wizard robes, we have some evidence that others weren't so lucky. We can imagine what it was like when fireworks and celebrations were all one could see to explain news that they hadn't heard. Strange sparks and lights were visible in regions untouched by man.
It's possible that not only were the Muggles terrified, but the world governments were frightened as well. Maybe there were cries of all kind, from "World War 3 has begun!" to "The Apocalypse is here!" Maybe ordinary people thought the spectafcles were a promotional event for something as ordinary as a new ice-cream flavor. The world was united in its confusion and some over-excited wizards were arguably making things worse by celebrating in ways never seen by any human eye.
The few Muggles who saw Hagrid flying with a baby in the air promptly dismissed it as a figment of their imagination and a sign of their anxious brains trying their hardest to find some rationality in the insane proceedings of the day. McGonagall saw it all as well and did her utmost to restrain herself from transforming back into her human form, Here Apparating to where those responsible where and giving them a peace of her mind.
Albus saw it all as well, but unlike Minerva, but perhaps, he merely smiled at the fireworks in the night sky, feeling the long-forgotten breeze of hope again. As he stood ready to go to Privet Drive and meet Minerva, he wondered how long the peace would last. Then, brushing aside his concerns, he Apparated to Privet Drive, holding a letter in his hand that would determine the trajectory of the one boy who changed everything. Harry James Potter.