A couple things to mention.
There is currently no consumer (or reasonably priced) Blu-Ray authoring program that allows you to import Dolby Atmos files. The only ones that do are the very expensive programs used by movie studios, etc.
One of these expensive programs, Scenarist, has recently started offering a subscription based plan, but I have no idea what the cost is (though it may be cheaper than buying it outright).
I believe these authoring programs have to pay a license fee to Dolby, which may be why they don't want to do it.
The best option I've found for Blu Ray authoring is a Windows only program called TMPG Authoring Works:
https://tmpgenc.pegasys-inc.com/en/product/taw6.html
This program at least allows you to import 5.1 PCM WAV files, for better surround sound quality than the Dolby Digital that most consumer authoring programs have. But that doesn't help you with Atmos.
Secondly, I'm not sure exactly what your workflow is, but I would suggest looking into Apple's Compressor application (assuming you're on a Mac) which is only $50, and that has a function to convert almost any format into H264. You may be better off importing a simpler video format into Protools just as a guide to do your sound work. When you're done, you can export the audio, then take your original quality video from DaVinci Resolve, convert it into H264 with Compressor, then import the video and the audio into your Blu Ray authoring application.
Note that Compressor does also have a very basic BluRay authoring function. No fancy menus, but just fine for burning a test copy, etc.
And yes, you can buy a blu ray burner and burn one off blu rays no problem. You could even send that burned disc to a replication plant and have copies made (up to a certain amount).
I got this blu ray/DVD/CD burner and it works great:
https://eshop.macsales.com/item/OWC/MR3UBDRW16/