Was the goal of extending liberty and justice for all successful during reconstruction?

Yes.

Explanation:

Yes, the goal of extending liberty and justice for all was successful during reconstruction because the African American got success in having the freedom in the south. the southern states accepted 13th, 14th, and 15th Amendments of US constitution. The period of reconstruction started after the civil war in which the union captured most of the areas of southern states and imposed laws of the union such as end of slavery and freedom of black citizens so we can say that  the goal was achieved during reconstruction.