Your favorite DAW app and an audio interface (or multiple) with enough outputs for the channel format you want to mix to. eg. at least 12 output channels for 7.1.4. There are some ProtoolsHD only plugins and they're pushing to lock this down as Protools only but you don't have to play along. We all already tend to use our favorite 3rd party joystick panner plugins. Or just draw automation. You can mix what you want in whatever DAW you want. It's just 12 channels of PCM audio (for 7.1.4).
If you want to deliver in the Atmos format (Dolby TrueHD 7.1 with the .4 height channels hidden in metadata) that requires the Atmos codec to decode, you need their encoder suite. This is where the push to keep this proprietary lives. Dolby sells a subscription to their encoder suite for $400/year and they give you a free media player that decodes the full lossless Atmos format that allegedly will keep working independent of their subscription scam.
You can set up speakers and start mixing right now. Delivering it in their 'ringer' of an encoded format is the stumbling point. Playing the files as a consumer is a big stumbling point at present with Dolby aggressively keeping the software hidden to push hardware sales.
I was wanting to do this the other way around...
Grab a few Atmos mixes first and hear what a couple people did. Day 1 would have been solo'ing pairs/arrays of channels on the 5.1 system. That was supposed to lead to motivation to hanging height speakers and throwing a couple sides in. Then finally listening to some mixes with a full 7.1.4 system. Now it's time to start making some mixes! Now follow up on required encoder software for consumer delivery.
Very difficult finding the motivation to jump in hanging speakers and mixing when the decoder is on lockdown and they're basically turning this into a form of copy protection. And with shitty stepped on streaming hash and seat of the pants remixes! Took the wind right out of my sails.
But there's literally nothing stopping any of us from setting up more channels and making some 7.1.4 mixes.
As I've stated you can mix for 7.1.4 now, and encode now to lossy atmos on Amazon's cloud. for a few pennies per track. Playback still requires something to decode the atmos...
I've mentioned a way to have one setup that plays both from your DAW, and from and AVR Preamp, using passive mixing balanced cables (ground lift on one side), or you can buy Radial mix 2:1 (x 12) if you don't want to solder your own, so you don't have to plug unplug 12 XLRs to change setups.
I've also mentioned you could use headphone virtualization, as a way to get started without buying and hanging speakers.
Top of the line would be a Smyth Realizer A16 an I actually use that 99% of the time vs. turning on the 13 Genelecs in the studio. Has to be heard to be believed, but that is covered in other threads...