Short answer: No — we do not have an original score written in Johann Sebastian Bach’s own handwriting for the Six Cello Suites. What survives are later copies made by other people.
What does “original” or “autograph” mean? An autograph is a piece of music written down by the composer himself. If we had Bach’s autograph for the cello suites, it would show exactly what he wrote and how he wanted the music to be played. For the cello suites there is no known autograph by Bach.
What do we have instead? Several early handwritten copies of the suites have survived. One of the best-known is a copy made by Anna Magdalena Bach (Bach’s second wife). She copied many of Bach’s pieces. There are also other copies made by Bach’s students or by professional copyists from the 1700s. Because these are copies and not the original, they sometimes differ a little from each other in notes, fingerings, and bowings.
How do musicians and scholars deal with that? Because no single original exists, music editors compare the different old copies and make careful decisions about what Bach most likely meant. These modern editions try to give performers a clean, reliable version of the music. Different editions can still have small differences depending on which old copy the editor trusts more.
Why are the suites so famous? The suites probably stayed quiet for a long time until the 19th and early 20th centuries, when cellists like Pablo Casals helped make them very popular. Casals discovered a copy of the suites when he was young, learned them, and performed them widely, which brought the music to the attention of the whole world.
Summary: No original manuscript in Bach’s own handwriting has been found for the Six Cello Suites. We rely on high-quality copies (including one by Anna Magdalena Bach) and careful scholarly work to know and play these beautiful pieces today.