I'd use a second table with a formula using OFFSET.
Entered into A1 on the target table and filled into row 1, it will return the values from column A in the source table.
Entered into A1 on the target table and filled into column A it will return the values from row 1 of the source table.
Adjust the $A$1 reference in the Source table to match the top left cell of the range to be transposed. ("Source" in the formula must match the name of the source table.)
Leave the formulas in place for continued transposition of the values or copy the target cells, then Edit > Paste Values (aka Paste Formula Results) if the values are to be moved or remain fixed when values in the target table are to remain constant if the source values later change.