Find out what spices were used

Yes, theoretically, and no for practical purposes.

Here's the Yes part:

If you have access to a chemistry lab, you can certainly analyze the dish for the presence of specific molecules that would indicate the presence of specific spices. For example, the presence of "cinnamaldehyde" would indicate that cinnamon was used.

Here's the No part:

First, you would need to do individual tests for each possible distinct seasoning molecule. Given the universe of spices, that's only feasible if you already have a pretty good idea of what's in the dish and are just verifying.

Second, some seasoning molecules are changed by cooking, making them less recognizable. Sugar particularly can change into dozens of different compounds depending on the cooking process.

Third, some seasoning molecules are just not that indicative of what the original seasoning was. For example, the presence of salt, glutamate, and various soy compounds would indicate the use of soy sauce, oyster sauce, or miso, but which kind of sauce exactly? That's leaving aside the difficulty of distinguishing various starches and sugars. Also, some spices come from the same plant (e.g. coriander seed and cilantro) and thus will be biochemically indistinguishable, even though their effect in a recipe is distinct.

So: ask the restaurant. It'll be way easier.