It is unlikely that they walked from Ukraine to Palestine during that period, especially after the beginning of WWI, since the Turkish/Ottomans were Germans allies, while the Russians were allies with France and England. Traveling as Russian/Ukrainian nationals through the Ottoman Empire during the war would mean death sentence or long imprisonment as spies, if caught.
As others have said, it is more likely that they sailed to Palestine from a port in Europe and part of their journey to that port may have been on foot. It is also possible that if they disembarked at Port Said (Egypt) or Beirut (Lebanon) instead of Jaffa, they had to walk the rest of the way. When my great-great grandfather immigrated from Belarus to Palestine in 1891, he left his wife and 4 younger children in Port Said and sailed to Jaffa with his older son. Once they found work and were able to rent a room, they sent for the rest of the family, but for some reason, the ship from Port Said did not stop at Jaffa as planned and continued to Beirut, from which they traveled by wagons to Palestine.
Most maritime traffic to Palestine stopped during the war, so if they did manage to get to Palestine, it was most likely before or after the war.
Cherry Hill, NJ, USA (formerly from Israel)
Researching Israelit (Belarus and Latvia), Goldblat (Belarus), Vilensky (Belarus), Pruss and Koifman (Ukraine)