You couldn't know exactly, but you could come close. Proteins are made up of long chains of amino acids. There are twenty different amino acids. Each is coded for, in DNA, by one or more sequence of three different nucleotides. Since some of the amino acids are coded for by more than one set of 3 nucleotides, you can't determine the exact DNA sequence. For example, leucine is coded for by 6 different 3-nucleotide sequences, so just knowing that leucine is in a particular spot in the protein chain doesn't tell you which set of 3 nucleotides gave that particular leucine.