Unless you're actually trying to cycle the aquarium to start the nitrogen cycle, the betta can go in almost immediately. The nitrogen cycle is more complex than pouring water in a tank and letting it run for a week.
It's also beneficial to know if you're going to be using tap water (chloramine that when broken down releases ammonia into the water) or a filtered or bottled water. Live plants will effect the cycle as well because they interrupt the nitrogen cycle by breaking ammonia down before the beneficial bacteria are able to do so.
Honestly, one betta doesn't produce that much waste and so long as you aren't grossly overfeeding, I'd set the tank up, let it run for 24 hours to be sure all equipment works, add betta, feed every other day no more than the fish can eat in 5-10 seconds, and on the days you don't feed do a small water change. Fresh water never hurt a fish. Once the tank is cycled, weekly water changes should be fine.
Also I'd recommend Seachem Prime as it is able to neutralize both ammonia, nitrites, and nitrates, as well as breaking down chlorine.
DT is mad iconic I love them sm
20 shrimps and Bob the snail are my cleanup team.
