You have some options.
You can go the Form1 route and SBR it. As soon as it's approved (6-8 weeks for a form 1) you can put as short a barrel as you want on it.
If it is not registered as an SBR, the barrel length must be 16". With a barrel less than 16" a muzzle device can be "permanently" attached to bring the barrel length to at least 16".
It can be "permanently attached by sweat soldering it on with high temp silver solder (melts at about 1360 degrees F). That's hot enough that removing the muzzle device with heat tends to screw up the barrel.
The other alternative is drilling the barrel and muzzle device part way through for a cross pin. That pin must then have a weld placed on top of the pin. If it's skillfully done and filed to the profile of the muzzle device it can be very hard to spot. Removing it then requires the weld over the hole be drilled out, so the pin can be pulled out. Easier than removing a silver soldered part, but still meets the requirements of not being readily removable with hand tools.
----
That said, I'm in total agreement that putting a brake on a .223 is a total waste of time - even on a competition gun.
For example I shot my first tactical rifle match around 1990, mostly because it was being held in the morning at a range where I was shooting my M1A in a High Power match that afternoon and I planned to use that for the "battle rattle" category, but I needed something for the light rifle portion. I didn't have an AR-15 at the time (and didn't really want one at the time). So I bought a nice surplus M1 carbine and the only 2 boxes of .30 carbine ammo the gun shop had (surplus Lake City ball ammo) and three 30 round magazines.
Early in the morning before the match, I took 10 rounds to zero the M1 carbine and confirm the adjustable rear sight was more or less on out to 250 yards (max distance for that match, with most of it 100 yards or less). I loaded up the other 90 rounds and registered for the match.
There were a number of people there shooting AR-15s in the light rifle class, and many of them had muzzle brakes. Most of the AR-15 shooters saw me as a total non contender. I ended up winning the battle rattle and I took second place in the light rifle division, with the first place finisher being the match organizer who was shooting an HK-93. In other words my old school M1 carbine beat every AR-15 in the field, including the race gunned muzzle braked AR-15s.
Eventually I switched to a heavy barrel AR-15 for high power competition and I also started using an AR-15 in tactical rifle matches. I had two that I preferred.
The first was an XM-177E2 semi-clone. It had a 12 inch heavy under the hand guards barrel for more stability in sustained fire and where longer ranges were in play.
The second was a lightweight 16" pencil barrel carbine with a fixed entry stock. With a slick side upper and carry handle sights, it's about as light as you can get without going to a composite lower.
You won't find a muzzle break on any of them, even the 5.7 pound pencil barrel carbine. it just isn't needed.
