There would likely be two of the same sphere in space
Something like that is probably so old that it existed somewhere at the time the movie took place. It was somehow captured, possibly allowed itself to be captured, and sat idle in the ship at the bottom of the ocean for at least 300 years. If it can propel itself out of the ocean and into space it could probably have gotten out of the ship at any time if it wanted to. Questions include: How fast it travels through space? If it's not moving anywhere close to the speed of light it would take a long time to travel between stars. Did it know that it traveled into the past with the ship? Does it have a concept of time? Did it maybe cause the wormhole? What are the chances than a human spaceship far out in space goes through a wormhole and they end up on earth? The ship had no log of traveling out of the wormhole or back to earth. It was determined that the ship wouldn't have survived the impact intact so it arrived on earth instead of crashing into the ocean. Could it be that he crew intentionally put the ship in the ocean & destroyed some log entries, possibly under the influence of the sphere?
Also, why wasn't there more exploration of the ship? It was said to be half a mile long. Was the sphere the only interested thing onboard? Surely it has a lot of advanced technology like artificial gravity, some sort of magnetic field to fend off space debris, a propulsion system that allows it to cross space in a reasonable amount of time, energy-based weapons, and something to prevent the crew from turning to a pile of bones & flesh when the ship came quickly decelerated.
(this signature was absent on picture day)