No, not as a core term. TST does not specifically adopt “existential givens,” or “facticity” as formal vocabulary. Those ideas are useful historical bridges, especially through Sartre and existentialism.
Existential givens usually refer to the facts you are born into or cannot simply wish away: your body, birthplace, family, time period, biology, mortality, and social conditions. Sartre called this kind of thing facticity. These are not choices, but they shape the field in which choices happen. You may feel free to drink water or not, but if you stop drinking water, you stop living. TST uses the common word circumstances, as in your birth circumstances, current circumstances, and upcoming circumstances.
TST keeps the useful insight but avoids making “givens” a separate core term. In TST, a person exists in a current state, with properties and relations already in place. Those conditions create constraints. Within those constraints, some potentials remain open and others are impossible. A human baby can become an adult human, but not a tiger.
So TST frames this topic through choice and constraint. You do not choose the full starting point of your life, but you do make choices from within it. Those choices actualize some potentials and close off others. Your life is not unlimited freedom, and it is not total determinism. It is a lived path through reality’s constraints.