Looks like you're off to a good start!
A couple things I'd add is that if you're just keeping fish and motile (moving) inverts and no corals, you don't need the Instant Ocean Reef Crystals salt mix. Regular Instant Ocean salt mix will be just fine for your fish, and cheaper to purchase.
What fresh water source did you use to mix with your salt? You can use tap water for a fish only tank, but keep in mind that if you do you will likely be battling some algae issues in a short while, which can be delt with in a fish only tank. If you did use tap water, give the whole system about 24 hours to run to make sure that no chlorine is in the water, then you can officially start your cycle. Or alternatively, treat the tap water with an aquarium dechlorinating product.
Many of us use a Reverse Osmosis filter followed by a DeIonization filter (RODI system) to make nearly pure freshwater that we then use to mix with our salt mix and to top off the tank. If you wanted to keep corals in the future, and RODI filter system is pretty much mandatory. For fish only, you can work with tap water, it just has some of its own challenges.
You mentioned that some of your rock is old and came from the Facebook Marketplace and that it's soaking now. If this was rock that was in an established aquarium for some time, but has now dried out, it is almost certainly loaded with dead organic material that if you were to just place it in your tank would cause an ammonia spike all on its own. Are you soaking this rock to remove those organics, which would be a good idea, in my opinion? If they are really bad, have you considered bleach curing your old rock?
If you're going to add real, quality live rock from your local fish store it will bring all the microbes you need, so there's no need for the Dr. Tim's One and Only in this case (though if you had a bottle on hand, nothing wrong with adding it). But, you need to get that rock in your tank, obviously. This would be the easiest and fastest way to get your tank ready for your Green Chromies.
If you're starting the tank now with your CarribSea sand and dry base rock, you'd be best to add the Dr. Tim's One and Only so you get a good population of bacteria initially.
Dr. Tim's One and Only, and other products like it such as Fritz Turbo Start, BioSpira, etc. are only adding the beneficial bacteria that you need for a healthy tank. Those bacteria now need something to "feed" on, so to speak. This is where you'll want/need some ammonia in the system to help get your bacteria colony started.
Ammonia can come from several sources during your nitrogen cycle, such as by adding a piece of shrimp from the grocery store or seafood market. The shrimp will break down in your tank, causing ammonia to rise, and the bacteria then can go to work. Likewise, you can ghost feed your tank by adding a small mount of fish food to the tank, as if there were fish in it. The fish food breaks down like the shrimp, and gives off ammonia. You can also add bottled ammonium chloride as a source of ammonia, which is what I prefer over the shrimp or ghost feeding method.
IMPORTANT: Ammonia can also come from using old rocks from another tank that have dried out.
I'm sorry this is so long, but all this is leading to my suggestion that you get a good ammonia test kit. I think you need to determine if your old rocks will be giving off ammonia. If they are, you likely don't need to add any more ammonia, but you won't know unless you're able to test your ammonia level.
Cycling is then just a matter of time and patients. There are products that can accelerate the cycle, like Fritz Turbo Start, but time does the same thing.
I hope that helps and I hope I didn't confuse you more lol! Please post back if you have any questions about what I'm trying to explain about your rocks.
Best of luck with your tank!