We had the same problem earlier this year, arriving on E2 in California. You will likely need the temporary insurance for 1-2 months, as you will require proof of address (I.e. lease and utility bills), evidence of being a new resident and other docs to get the permanent one, and there can be a lead time to start (in our case they were only able to start on the 1st of the month after approving us).
In my case in California we used GeoBlue for the temporary one. I had called BlueShieldCA sales from the UK, and they recommended GeoBlue for this. Make sure you read the plan you sign up for in detail to make sure it is valid for the temporary circumstances (not many are - for example most travel insurance isn’t) and get on permanent health insurance as quickly as possible.
I didn’t have any claims, but can recommend GeoBlue in terms of being good to deal with. They were flexible to let me cancel the monthly plan at the end of the month at short notice when I finally had the permanent health insurance sorted. We paid about $900 per month for two adults.