When do I switch the SIM card when transferring to a new phone?

I have just had my iPhone 11 pro max delivered and I am switching from my old iPhone 7+. I have backed up my 7+, unpaired my apple watch and now am at the point when I need to transfer the data. When do I take the sim card from my old phone and put it in my new phone? Can I leave it in the old phone and do the transfer and then put it in the new phone once it already done. I've had one failed attempt as I forgot to back up and unpair my watch but the screen recognised the circle of dots and started the transfer. I stopped this as I hadn't backed up but when I looked it said I should swap the sim. When I did this the phone didn't recognise the circle and asked me to manually set it up which when I tried said it couldn't. Help!!!! I did get a new sim with the phone but I will switch that over once I have sorted this problem out. Thanks.