Hi and welcome to the forums!
I think from keeping a goldfish in a small tank, as you've stated, yes, it's growth will probably be stunted, so the fish will quite possibly grow at a slower rate than a goldfish of the same age kept in a larger tank.
I personally kept a goldfish in a 21 litre tank for around 5 months where she grew an inch or two (she was around 3 inches in total by this point) she's now in a 90 litre/3 foot and has grown around 1/2 an inch, in the 2 months she's been in there.
Seeing as your goldfish has been in the 1 gallon tank for a small time and I imagine will be moved very soon, he should be fine
As long as you see no outward or behavioural signs of him being unwell, as often fish kept in small aquaria have generally had to put up with poor water quality and can have some problems because of this.
Do you have a water test kit or a pet store that can test your water for you? This can be really helpful with knowing when the tank has completely cycled
It could also help on knowing what the water quality on your 1 gallon tank is like, if the water quality is bad i.e. ammonia/nitrites present, or nitrates being above 40ppm, then you may need to do more regular water changes while the bigger tank cycles.
Best of luck with cycling! Look forward to seeing some photos