Vena cava is valve less. So, during atrial systole what prevents backflow of blood to them?
Pressure differences. Atrial contractions are much more gentle than ventricular ones, and in normal circulation the venous pressure in the vena cava often stays higher than the right atrium, even during atrial systole. If the pressure in the atrium does rise above the vena cava pressure at the peak of systole, there can be some backflow, although it is slight and brief in normal physiology.
The major veins are typically somewhat distended so they are constantly pushing blood into the right atrium. Blood continues to flow from the veins into the right atrium and from the right atrium into the right ventricle throughout ventricular diastole, including during most of atrial systole.
Besides @Bryan Krause answer, there's another very important factor that prevents the blood from flowing back from the right atrium to the vena cava during systole.
Part of the muscle that constitutes the atrial walls also wraps around the site of entrance of the vena cava. Thus, during systole, the muscle contracts, closing (or almost closing) the passage and doing the job of a valve.
EDIT: because of the high skepticism over what I have said in this answer, and having no references, I went to search for the class where I studied this, and here's the slide containing the information. Unfortunately, it is in Portuguese, but I will translate what it says, and you can check in any translator.
Venous myocardium: Cava Veins and Lung Veins
The veins that open in the heart don't have functional valves, meaning that the atrial systole could cause blood backflow through these veins.
Venous myocardium: The cardiac muscle tissue is prolonged through the vein walls that bring blood into the atrial cavities to the point of insertion of the fibrous pericardium.
Physiology: The venous myocardium contracts at the same time as the atrial wall, preventing the backflow of blood to the veins during atrial systole.
The atrial pressure when equal to that in the incoming vein will contain blood which will be propelled into the right ventricle without the need for any increased pressure [as does the ''muscular pump' in the body. In other words the right atrium is ' functionally a sophisticated valve'