"Graduate visa holders are able to work flexibly, switch jobs and develop their career as required. When your Graduate route permission is issued you can do any work, either employed or self-employed, except working as a professional sportsperson or coach. You can take work at any level of salary or skill. If your plan longer term is to find a job for which you can eventually be sponsored under the Skilled Worker route, you should check which jobs are eligible for that as you will need to meet certain salary and job level requirements for that route when your Graduate visa expires.

Employers know about the Graduate route, and they should understand that with this permission you can take any work you wish without sponsorship and without any special actions for the employer. If they are unsure you can refer them to this guidance from the Home Office for employers where a specific section on the Graduate route explains that:

"The Graduate route enables international students who have been awarded their degree to stay in the UK and work, or look for work, at any skill level for two years, or three years for doctoral students. It is an unsponsored route, meaning you do not need a sponsor licence to hire someone with a Graduate visa."

Excerpt from UKCISA.org

I was born and raised in Southern California and the Southwest. I do not require any sponsorship to work in the USA.