Why did people cross the land bridge?

For the same reason humans migrated to anywhere else on Earth from Mesopotamia. We(modern humans) are not exactly sure why our ancestors did this. A popular theory is that they were searching for more land to live and farm. For example: If someone builds a house, their descendent can't build another one in the exact same spot. So they have to find a different spot. So they built houses, planted crops, etc and it would grow into a city. Over time, humans spread accross the globe like this.