With a fish-in cycle, you need to do a water change whenever you have a reading for ammonia or nitrite above zero. Both of these are toxic to fish and will shorten their lives, if not kill them, if they remain in the water. Water changes are your friend when cycling with fish. The water changes need to be often enough and big enough to keep both ammonia and nitrite as close to zero as possible. Even trace amounts in the water will encourage the bacteria to grow.
There are things you can do to help.
Add Tetra Safe Start or Dr Tim's One & Only. These contain the bacteria we want to grow and will speed things up.
Use a water conditioner which 'detoxifies' ammonia. Seachem prime also detoxifies nitrite. The detoxification only lasts 24 to 36 hours so you still need to do the water changes but the water conditioner will keep the fish safe between water changes. Ammonia and nitrite will still show in the tests with these water conditioners.
Feed the fish once every 3 days. Less food = less ammonia making it easier to keep the two poisons very low.
Put live plants in the tank. Plants use ammonia as food and they don't turn it into nitrite. Floating plants are particularly good for this.