The first place recruiters go to source for positions - especially for those that are harder to fill - is LinkedIn.
So no: you absolutely don’t need to have LinkedIn to get hired if you apply directly. LinkedIn makes it easier for companies to find and contact you.
Anecdotally, my last three jobs in my career have come from LinkedIn outreaches (Skype, Skyscanner, Uber). These were opportunities I would have not come across, as I was not actively looking, but they found me at the right moment. Before I always applied directly.