Are you kidding? Of course not.

What is a digital signature?

Digital signatures use the holder's private key to encrypt data, because the private key is only owned by the holder and cannot be forged by others, while the public key is public and is used by others to verify the signature.

If it is a symmetric key, then there is only one key. Do you make this key public? If it is not made public, how can others verify it? If it is made public, anyone can forge your signature.

This is a basic concept issue that needs to be understood well.