I'd go ahead and add the whole first initial shot of Ammonia. Use the Aquarium calculator to work out the amount you need, and add slightly less. It takes usually about a week for the first hit of Ammonia to drop anyway, so you may as well get started while you await the test kits, saves waiting later
Done properly, a fish in cycle is not cruel. The idea is to do enough regular water changes to control the amount of ammonia and nitrites that build up during the process of growing your bacteria. A long slow cycle is not harmful to the fish. Getting impatient and forgetting to do water changes is.
Up until the last five years or so, tanks were always cycled with fish. Then, someone invented the fishless method. Personally, I've never used it, and doubt very much if I ever would.
Disagreeing with a mod usually isn't recommended, but...
No matter how you fish-in cycle, you
always intentionally subject fish to some levels of poisonous chemicals. It does not matter how carefully you manage the cycling process, you will always do it, unless the tank is really heavily planted under an EI regime and plant growth is coming through strongly. Research as apparently shown that above 0.25ppm of Ammonia or Nitrite is harmful in the short-term at neutral pH. Any detectable reading in the long-term will lead to damage to the fish. What is defined as short- or long-term is sketchy however, short-term usually between an hour or two to a day, and long term being anything from 4-8 weeks. A cycle takes about 4-6 weeks, and you constantly have at least traces of Ammonia or Nitrite during this time unless the tank "silent cycles" in a heavily planted set-up. This means that in almost all controlled fish-in cycle situations you do damage to the fish, permanent, lasting damage.
I'm not saying I'm totally against fish-in cycling. I've personally done it on a number of occasions. However, for almost all fish now, I will fish-less cycle, purely because I know what I would be doing to the fish by subjecting them to a fish-in cycle
If you do have access to an established tank, be it goldfish or tropical, it's entirely possible that you can start up a new tank by "cloning" it from the older one.
Now there is a good suggestion
Alot of people dont realise that you'd need a 200ltr+ tank just for 3 goldfish!
As someone that's bred Goldfish in the past, I'd argue that they are not tank fish. All my brood stock were stunted by tank life when the spawned, and they were all in excess of 18" in length. A Goldfish in the correct conditions, believe it or not, will reach about 3 foot in length

Fancy Goldifish, in larger tanks, I don't mind, but I would never keep common Goldfish in a tank again, only in a pond
All the best
Rabbut