The first things about the photo that struck me was a) hair length b) clothes.
Olga and Tatiana both have their hair up, indicating that it has to be at least 1913. Marie doesn't have her hair up meaning that it has to be before June of 1915, because Marie would have been 16 then. Also, during the war, Alix didn't buy the girls new clothes and the trend of their fancy matching outfits generally disappears. Alexei also started to wear uniforms instead of sailor suits to support the Russian army. My best guess would be either right after the start of the war--autumn, early winter of 1914--or sometime before August 1914, perhaps the spring.
The Empress' devotion to nursing began as early as the end of 1914, so she, Olga, and Tatiana would probably have been wearing uniforms if it was taken in 1915.