Sulkiewicz was born in Skirsobole Tatarskie, Congress Poland (now part of Lithuania) to a Tatar family with a tradition of support for the cause of Polish independence. He was the son of Aleksander Sulkiewicz, a "rotmistrz" in the Czarist army, and Rozalia Sulkiewicz (née Kryczyńska—the feminine form of Kryczyński, one of the few Tatar families officially acknowledged as princes by the Polish–Lithuanian Commonwealth). His grandfather was Józef Bielak, a general in the Kościuszko Uprising, and one of the family's most cherished possessions was a letter from Tadeusz Kościuszko thanking Bielak for his service.