If we can agree that if a two systems are in the exact same state then they will continue to be in the same state in future, then we can say deduce that the universe is deterministic.
If a player hits a snooker ball exactly the same way two times, and all other balls are in the same position, the temperature is the same, humidity is the same, rotation of the earth is the same, rotation of electrons and unknown state of quarks are the same -- everything is the same -- then the result will be the same. To have a different outcome from the same inputs in a closed system is not possible.
The same goes for human thought. If your brain is in the same state twice, all neuro chemicals are in the same state and all external forces are the same, and you are posed with a problem twice, you will make the same decision twice. There is no other possible outcome, for if there were another outcome it would be due to a differing influence. Thus your decisions are effectually predetermined.
This the universe in its current state can only move forward in one way -- effectually predetermined.
If anyone can come up with a case that two closed systems that are in the same state can diverge, I'd love to hear it.