Although they both deal with time, these are very different words.
Early has two basic meanings:
1. Not many hours after midnight.
Since I start work at 7:00, I have to get up early every morning.
In the temperate zones, the sun rises very early in the summer.
2. Before the scheduled or expected time:
I try not to arrive at parties early, so the hosts have time to get ready.
It is far better to be early for an appointment than late.
Soon means in the near future.
Since my birthday is this Wednesday, I will be 59 years old soon.
Look at the sky. It �s going to rain soon.
"Sooner than expected" means the same as "early".
Bruce