It is hazardous to take upon oneself the interpretation of Heidegger. But I know his use of the phrase 'always already' and offer my explanation.
Dasein, taken as the presence or reality of a human being, is 'situated' right from the start. It is 'Being-in-the-world'. It is 'always already' situated in a socio-historically shared world (Mitwelt) into the norms and conventions of which it is initiated. It does not come into being gradually, passing through successive stages of development until it achieves its mature form. As soon as we are conscious of ourselves and our environment, it is 'always already' present.
From this 'always already' initial situated state, a human being self-constructs by projecting itself onto the possibilities of its world, or less obscurely and more specifically by entering into socially and historically 'possible ways for it to be', adopting socially and historically roles and relations, and interpreting its surroundings and itself in those surroundings in socially and historically possible ways.
Far more could be said but perhaps this gives you a slight first grasp of what this mysterious phrase 'always already' means.
Heidegger, M. (1962). 'Being and time' (J. Macquarrie & E. Robinson, trans.). New York: Harper & Row, p. 65.
Aret Karademir, 'Heidegger and Foucault: On the Relation Between the "Anxiety–Engendering–Truth" and "Being-Towards-Freedom"', Human Studies, Vol. 36, No. 3 (Fall 2013), pp. 375-392.