Hi bettajune,
Sorry, but you're going to have to do this the hard way. The wireless charging coil is integrated on the same flex cable as the power and volume buttons, so those have to come up at the same time. In addition, the adhesive that holds the coil in place extends out the sides of the coil and there's no way you're going to get it in place without removing the battery. Finally, as @strongbow already mentioned, you have to have the battery out in order to route the power connector to the motherboard.
The bad news here is that as far as I can tell, nobody has written a guide for the repair you need to do. I wrote the wireless coil replacement guide for the iPhone X, so I'd suggest taking a look at that one to give you an idea of what has to be done, but there are obviously going to be differences in the procedure, just like every phone is different.
iPhone X Charging Pad / Volume Button Assembly Replacement - iFixit Repair Guide
One of the great things about iFixit is that anyone can author a guide. You can use existing guides as prerequisite steps to build your guide on other people's work; that's exactly what I did with the one I wrote. If you wanted to contribute to their repair efforts, it would be great for you to take pictures and document your steps and create your own guide for people who come after with the same problem. I'd be more than happy to help out as well if you decide to.
I've got a couple more guides that describe the process for removing the rest of the components necessary in order to get to the charging coil and buttons. Not all parts will necessarily need to be removed; you'll have to be the judge of that since you're blazing this particular trail. The first is a teardown guide from here on iFixit.
iPhone 12 Teardown - iFixit
The next one is a rear case replacement guide from a French site called SOSav.
Frame iPhone 12 repair - Free guide - SOSav
Unfortunately, the charging coil is one of the harder repairs to do, mostly because of the amount of parts you have to remove just to get to it. I'd suggest getting the buttons in place as much as possible before gluing down the coil itself; you don't want to have the coil slightly out of place and the cables not be able to reach where they need to go. Same for the connector to the logic board; before securing the coil reinstall the logic board temporarily and plug in the connector before finally gluing down the coil. Yeah, I learned that one the hard way, so don't be me, lol.
Good luck with this one; I'd love to hear what you decide and how it goes.
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