There are only three ways of completing a proof:
The circular argument, in which the proof of some proposition presupposes the truth of that very proposition
The regressive argument, in which each proof requires a further proof, ad infinitum
The dogmatic argument, which rests on accepted precepts which are merely asserted rather than defended
This is a dilemma for classical logic in particular; it could be addressed by introducing nonmonotonic logic (default and challenge). Some claims (e.g. first person observations) come with a default justification (which is not based on the justification of other claims). Yet it must be defended when challenged.