The Verdict: Unlikely
You cannot apply without a licensed sponsor, so finding one is the first step. Search the Home Office register of licensed sponsors, and check the routes that need no sponsor at the same time.
An employer not on the register cannot sponsor you unless it applies for a licence, which takes months and which most small employers will not do for one hire. Target licensed employers and ask about sponsorship in the first conversation.
The job will need to be at graduate level, paying at least £41,700 or the going rate, and you need English at B2.
Routes with no sponsor: Global Talent, with an endorsement or qualifying prize; UK Ancestry, with a Commonwealth nationality and a UK-born grandparent; and the Youth Mobility Scheme, if your age and nationality fit.