unless you are ready to spend upwards of $1000 on rent I do not think you should consider moving at the moment.

you're likely going to be working from home anyways, and honestly the cost of living in LA during a pandemic is not worth it. Cases are high here and we are probably going to be stuck like that until next year. So you will be paying to live in a small room and spend 90% of your time there. If you would be living with family or a close friend then perhaps? But I can imagine LA being miserable without friends, family, or a good social support network... and no feasibly safe way of meeting people.

Wait for the job offer to be on the table before you move out here. We are in the early stages of a recession and that job offer could come in 6 months or a year. Additionally I would think landlords would be more skeptical of renting to a recent graduate with no job. I've seen some landlords request a 6 month security deposit.

I'm really not trying to bring you down, but things are not that glamorous in Los Angeles right now. It would be very risky to move out here with out a solid plan and safety net (financially and socially)