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• Different Constellations: You are on any non-Earth planet.
• More and Brighter or Less and Dimmer stars: You are on a planet closer to or farther from the galactic center.
• More and Dimmer or Less and Brighter stars: You are in a more or less differentiated part of the galaxy.
• Green Stars: Since the physics of this place are not so different that I am instantly dead, I'm gonna assume a world with a different atmosphere or nebula gasses that filters the starlight, or I might mistakenly believe that a visible star might be able to achieve a doppler effect of a red star getting closer or blue star moving away... something someone with some but not advanced knowledge of astronomy might think.
• Stars don't move at all:** The planet has a negligible spin relative to the galactic background.
• Stars move fast enough to see move or orbit in different directions from one another: Those are just tiny moons reflecting the sun.
• Stars don't move in smooth curves: This planet has a strong wobble.
• Stars move completely randomly: Clearly, I am hallucinating. Avoid eating any more suspicious plants.

• Different Constellations: You are on any non-Earth planet.
• More and Brighter or Less and Dimmer stars: You are on a planet closer to or farther from the galactic center.
• More and Dimmer or Less and Brighter stars: You are in a more or less differentiated part of the galaxy.
• Green Stars: Since the physics of this place are not so different that I am instantly dead, I'm gonna assume a world with a different atmosphere or nebula gasses that filters the starlight, or I might mistakenly believe that a visible star might be able to achieve a doppler effect of a red star getting closer or blue star moving away... something someone with some but not advanced knowledge of astronomy might think.
• Stars don't move at all: The planet has a negligible spin relative to the galactic background.
• Stars move fast enough to see move or orbit in different directions from one another: Those are just tiny moons reflecting the sun.
• Stars don't move in smooth curves: This planet has a strong wobble.
• Stars move completely randomly: Clearly, I am hallucinating. Avoid eating any more suspicious plants.

The final nail in the coffin of your reality will be when you encounter people or wildlife that are not where, who, or how they should be. This could fully disprove time travel leaving jumping into an alternate reality (aka: another universe) as the only possible option left... that, or maybe hallucinations or a dream, but at that point, you've been in this place for way too long and thinking way too clearly for that to sound right.

The final nail in the coffin of your reality will be when you encounter people or wildlife that are not where, who, or how they should be. This could fully disprove time travel leaving jumping into an alternate reality (aka: another universe) as the only possible option left... that, or maybe hallucinations or a dream. Different people have different breaking points of disbelief; so, at this point it becomes an author's choice if your protagonist feels more comfortable believing that he is in an alternate universe or that he can simply not trust his own senses.

• Different Constellations: You are on any non-Earth planet.
• More and Brighter or Less and Dimmer stars: You are on a planet closer to or farther from the galactic center.
• More and Dimmer or Less and Brighter stars: You are in a more or less differentiated part of the galaxy.
• Green Stars: Since the physics of this place are not so different that I am instantly dead, I'm gonna assume a world with a different atmosphere or nebula gasses that filters the starlight, or I might mistakenly believe that a visible star might be able to achieve a doppler effect of a red star getting closer or blue star moving away... something someone with some but not advanced knowledge of astronomy might think.
• Stars move fast enough to see move or orbit in different directions: Those are just tiny moons reflecting the sun.
• Stars don't move in smooth curves: This planet has a strong wobble.
• Stars move completely randomly: Clearly, I am hallucinating. Avoid eating any more suspicious plants.

It will actually be the fact that the stars remain the same that your protagonist can rule out most other possible explanations of what is happening to him, and it will be the little epiphanies of his journey slowly invalidating his expectation of the stars that will lead to the rising action of realizing something is off instead of there being something about the stars themselves that should be immediately evident.

• Different Constellations: You are on any non-Earth planet.
• More and Brighter or Less and Dimmer stars: You are on a planet closer to or farther from the galactic center.
• More and Dimmer or Less and Brighter stars: You are in a more or less differentiated part of the galaxy.
• Green Stars: Since the physics of this place are not so different that I am instantly dead, I'm gonna assume a world with a different atmosphere or nebula gasses that filters the starlight, or I might mistakenly believe that a visible star might be able to achieve a doppler effect of a red star getting closer or blue star moving away... something someone with some but not advanced knowledge of astronomy might think.
• Stars don't move at all:** The planet has a negligible spin relative to the galactic background.
• Stars move fast enough to see move or orbit in different directions from one another: Those are just tiny moons reflecting the sun.
• Stars don't move in smooth curves: This planet has a strong wobble.
• Stars move completely randomly: Clearly, I am hallucinating. Avoid eating any more suspicious plants.

It will actually be the fact that the stars remain the same that your protagonist can rule out most other possible explanations of what is happening to him, and it will be the little epiphanies of his journey slowly invalidating his expectation of the stars that will lead to the rising action of realizing something is off instead of there being something about the stars themselves that should be immediately evident.

What if you need the stars to be different for plot purposes?

If you can't rule out all other possibilities, then give your protagonist a reason to place inter-universal travel as a more likely conclusion. In real life, the idea of interplanetary travel seems the most possible because other planets are things we can see and measure whereas other universes only exist in vague theoretical terms. However, if the scientists in your world have already made functional inner-universal looking glasses to see into and confirm the existence of other realities, then even if inner-universal portals are not yet a thing, the possibility of inner-universal travel would suddenly seem far more conceivable.

There could even be published papers based on scientific observations about what makes these other realities unique from our own. In this case, whatever is different with the stars could be exceedingly subtle, but still enough to clue in your traveller because it would be the exact thing he'd be looking for. If you go this route though, there is no "best possible answer" to your question, because it would be up to you to come up with what science has defined as the key difference between realities.