Congress authorised the project in 1928. The great depression started in 1929. The construction began in 1931, some of the techniques were unproven at the time and the conditions were torrid. The great depression lasted another decade and FDR issued the first "New Deal" policy afterwards in 1933-34. The damn was completed in 1935.
He may not have been president whilst it was authorised, but his execution clearly sustained the great depression, when he should have postponed the project or set up a "new deal" like FDR did.