Are there citizen punishments that can be levied when a company refuses the law? For example, you put in a GDPR deletion request. Company ignores or otherwise

Are there citizen punishments that can be levied when a company refuses the law? For example, you put in a GDPR deletion request. Company ignores or otherwise does not comply with the law. Can you sue them directly over that? In the USA, Ive seen a lot of various laws like CAN-SPAM act. But there are no remedies for citizens who were spammed to get statutory damages for being violated. Having that option to get money for being wronged would solve these sorts of problems.