Yes, there is a 13th century great helm in the Deutsches Historiches Museum - originally found in Schlossberg bei Dargen, Pomerania. Claude Blair and others date it to the second half of the 13th century. Note that unlike earlier great helms (such as thise illustrated on the West Front of Wells Cathedral) it has the beginnings of a truncated cone skull top, which you see more pronounced in the 14th century. Unlike 14th century great helms it does not extend very far down to protect the throat.

In addition to this example, there is one in the Castelo Sant'Angelo museum that Alan Williams and Blair both date to the turn of the 13th/14th century.

Though your title mentions great helms before the 14th century, your body text mentions before 1400, so I will also address that. There are a number of great helms dating from around 1300-1400. A famous example is the Pembridge Helm at the National museum of Scotland. It is made of fewer pieces of metal (only 3 sheets) and has a face mask that dips to protect the throat, and a very high, tapered crown of the skull piece. It dates from around the middle of the 14th century.

References for further reading:

Claude Blair - European Armour 1066-1700 - a good overview of armour in the Middle Ages and Early Modern period. It describes the development of the Great Helm and includes pictures of at least 6 examples in the back.

Edge and Paddock - Arms and Armour of the Medieval Knight - covers any of the same subjects, but it is more recent and has more illustrations.