These are in progress and subject to revision. Feedback welcomed.
If the universe is eternal, then the universe would have already reached a metaphysically possible state for: (a.) a physical law to emerge or be realized that prescribes or describes that the universe enter a state of absolute stasis, where all future action is prohibited and the universe is compelled into complete immobility and unchangeability, or (b.) a meta-law or principle to emerge or be realized to prevent further changes to the physical laws while allowing changes to matter and energy.
A metaphysically possible state of the universe is one that is: (a) is not logically self-contradictory and (b) adheres to eternal or necessary truths (e.g., a triangle must have three sides and cannot have four).
The universe is not currently in a state of absolute stasis, and there is no convincing reason or scientific evidence to believe such a meta-law or principle exists.
Therefore, there is no convincing reason or scientific evidence to believe the universe is eternal. (Modus Tollens)
Time began with the creation of universe
This is not directly an argument against an eternal universe, but shows that if God exists, then time has not always existed.
The creation of the universe caused or resulted in a progression of one state of reality to another to take place.
Time is a progression of one state of reality to another.
Therefore, the creation of the universe caused or resulted in time to take place. (Definition Substitution)
If time (or the indefinite continued progress of existence) is a necessary precondition for the act of existence, then a necessary precondition for the act of existence has not been met if time doesn’t exist until it has been created.
Time is a necessary precondition for the act of existence.
Time does not exist until it has been created.
Therefore, a necessary precondition for the act of existence has not been met.