it would help to know jurisdiction/market area because that really affects the options, especially because that's a rapidly changing landscape right now. some places, prepaid SIMs + cash work well enough, other places it's better to go with giftcards or prepaid debit cards etc. yet other places there's definitely no good options to do it. it takes a lot of effort, and you have to remember that you need to consider that any app or service you log into on that phone may end up identifying you against the SIM card, so you need to be really careful in your usage! i hope you find an option that works! :)
I recall hearing a story about law enforcement identifying an otherwise-anonymous phone by other phones that pinged the same cell towers at the same times. Essentially, the person had two phones on them, so they were able to uniquely identify the individual based on the shared location history of the two devices.
So there's that, too, assuming my memory isn't just some CSI bullshit. (It seems reasonable that this attack vector is technologically possible, though, and it may not matter if it's legal if the identification technique isn't used as evidence in court.)
Reminds me of this doc I watched a couple weeks ago.
TLDW; psyco travelled across the country to kill his mom, then drove back. He bought a burner phone at the start of his trip, but kept his normal phone with him the whole time. The cops were able to track both devices as they each connected to the same cell towers while traveling together from the west coast, to the east coast, and back again.