This is a hypothetical:
The president has a right to pardon any federal crime. If the president pardons you for illegally entering the country, can you begin immigration proceedings as having never entered the country illegally?
Just to be absolutely clear this question is alluding to the president providing a blanket pardon. I, the person asking, want to get away from the politics of it and merely handle the legality: whether or not the implications of a blanket pardon will be sufficient to begin immigration proceedings for undocumented immigrants and what that would look like. For these reasons, I'm asking the question as a hypothetical about one person.