It is technically possible to take amtrak from DC or Alexandria but good luck meeting that timetable depending on when your flight lands.
This is not close. The best way this is at all feasible is if you rent a car and drive. The train runs 2-3 times per day from DC union station with the last at 5 on some days and 2 on others. There is a bus component of most train rides. That means if your flight is not in early morning or at least landing before 12 noon, you could lose a full day of your vacation trying to coordinate with the train and may have to spend a night in DC to catch it. The ride is also 6 hours so event in the best conditions you spend a day getting there and at worst 2 days
But you can drive there in four hours. If it's the middle of the day, the traffic won't be so bad. But it is 200 miles. And it's all highway, so it's hard to get lost. There are no tolls, but avoid any left lane lane entrances that require what's called an EZ-Pass; the other lanes on the roads will be free. If for some reason you do take the train, it deadends 20 miles from the ocean, and bus gets you the rest of the way.
Driving is a lot easier,if you can do it (not everyone likes to drive in a foreign country, but the US is a lot like Western Europe for driving), And you can use the same car to go back to Dulles, and to drive around that area of Virginia, which has some interesting places besides the beach. Of course it may be too expensive for you.
Just a question... Why did you pick VA Beach as a place to go? Not too many people from other countries even know that great beach area exists.