GAC is granular activated carbon.
New tanks at least until the full cycle is complete generally do not need to run any chemical filtration or active fuge. They like an over-sized skimmer will pull out too much and could lead to minor/major issues early on. Most recommendations are to wait on starting GAC for at least 2 months and 4-6 months for the fuge.
The full cycle is not just the Ammonia --> Nitrite --> Nitrate stages, but also includes the diatom and green hair algae, cyano stages which can take an additional 1-3+ weeks. These last two are affectionately known as the ugly phases. Diatoms are harmless feed mostly on silicates from the sand and rock and will cover nearly every illuminated surface. Keeping the main lights off during this phase will help to some degree but they do not need the light. You can clean the glass with algae sponges, add trochus snails, as well as syphon them off of the sand bed with a gravel vac, but as the silicate levels drop they will die off on their own. This is where weekly water changes is vital on a new tank. As the diatoms die off they will cause your nitrate and phosphate levels to start increasing. You want to keep them low, to prevent a green hair algae outbreak. After the diatoms is typically the cyano, GHA phase. This is from the nutrient levels being out of balance and lack of bio-diversity. Various forms of nuisance algae and cyano will make their way into the tank from the addition of your cleanup crew, as well as when you start adding corals. Much of this phase can be avoided if you remain patient and give the tank an extra 3-4 weeks after the initial cycle is complete before you turn the lights on and start adding fish. Then when you do go slow with only adding 1-2 smaller fish a week to allow the tank to adjust to the new bio-load.
Running carbon and/or an active fuge at this point in the tank's life can easily become more detrimental than beneficial. The carbon can and will strip too much out and the macro algae could easily strip the tank of nutrients, and this can open the door for a full blown dinoflagellate outbreak. Trust me you want to avoid a dino's at all costs. They have likely caused more hobbyists to do complete shutdown/restarts or just give up and walk away than any other issue. Dino's are a single celled organism that are toxic to most tank inhabitants, nothing will consume them and if an outbreak occurs it can easily take months to beat it back. Outbreaks can happen in both new and well established tanks, and almost always is the result of allowing the nitrate and phosphate levels to drop to zero or near zero as to be undetectable when testing for them. When the nutrient levels are that low for a sustained period, many types of bacteria that feed on them will go dormant and no longer out compete the dinos. The dinos then rapidly multiply causing the brown snot bubbles to start appearing and once this happens the other forms of bacteria struggle as long as the nutrient levels remain extremely low. To beat the dinos back, you have to ID what strain it is, then use multiple methods of attack to beat them back. This includes manually elevating the nitrates, and phosphates that can stress corals, UV, daily dosing of various bacteria cultures, manual removal, 3 day black-outs, etc etc. When I had a dino outbreak it took about 3-4 months adhering to a strict daily regimen from onset before I had finally beat them back.
I know it's agonizing sitting there looking at an tank for a month or more with just water and a few snails/crabs. You want nothing more than sit back and admire your own beautiful slice of reef like the pictures/videos you have been looking at that was part of the reason you got into the hobby. Just know that nearly every single one of those tanks went through many setbacks, took time in some cases years to get there. If you try to rush the tank, or get too lax on the upkeep, you will almost certainly be met with problems and frustration. Take your time, keep doing your research, don't be afraid to ask questions on here as well as at your LFS.