No, you cannot apply for a UK Skilled Worker Visa without sponsorship. You must obtain a valid Certificate of Sponsorship (CoS). A UK work permit requires this certificate because it serves as official documentation which includes your position information and pay details that support the UK points-based immigration framework.
Those who plan to relocate to the UK without employer support should explore alternative visa possibilities such as the Global Talent Visa and High Potential Individual Visa and the Graduate Visa (if they qualify). The Skilled Worker Visa program strictly requires sponsorship.