Does God Leave the Earth to Run on Its Own After Creating It?

No. He continues to sustains it. Provides for it.

Ps 104:14 "He causes the grass to grow for the cattle and vegetation for the service of man that it may bring forth food,"
104:19 "He appointed the moon for seasons, the sun knows its going down,"
104:21 "The young lions roar after their prey, and seek their food from God."