Nearly 100% of people who receive a DMCA notice of alleged infringement (read: 'copyright strike') from YouTube have the option of filing a counter-notification.
In nearly all cases, YouTube responds to valid counter-notifications by informing the party that initiated the takedown. Counter-notification starts the clock on a 10-day window, within which the party alleging infringement must - if they want to keep the video down - sue you in federal court and prove to YouTube that they they have filed suit against you. Otherwise the video goes back up.
That procedure is almost always available. The downside, of course, is that you might get sued for an enormous amount of money that you may be held liable for. Statutory damages are scary. (But thy are a consequence of infringement, not notice-and-takedown.)
When you issue a DMCA notice, you're certifying that the content is yours, under (theoretical) penalty of perjury. But big content studios erroneously issue them using automated systems all the time, and the only way to actually enforce this is for you, the individual getting targeted by one, to personally take legal action against a multinational corporation.
Meaning that, for all practical purposes, the people this affects have zero recourse.