Yes, we can keep fish in an uncycled container indefinitely by doing water changes very day or even every other day. It depends on the size of the fish and of the container. However, it is important to realize that a cycle becomes established because there is ammonia. Water changes reduce ammonia and this will greatly slow or prevents a cycle from establishing.
Doing the above is fine while one is cycling a permanent tank. Doing it for extended periods is not a great plan. Plants do use ammonium and nitrate. But if they were enough to handle ammonia, there would not be any nitrifying bacteria.
I would suggest one can greatly accelerate a cycle by using bottles bacteria of the proper kind. To me this means Dr. tim's One and Only and maybe Tatra Safe Start or Safe Start+. I am very familiar with the first product as i have used it off and on for many years. The other method is to use established tanks to supply seed bacteria. The easiest way is to rinse out media from a cycled filter. But the bacteria live on other hard surfaces of a tank as long as they are in subdued or absent lighting. Live plants also host bacteria.
Yes bettas can manage is oxygen poor environments. But they are not going to have toxic levels or ammonia or nitrite.
Kajimura M, Takimoto K, Takimoto A. Acute toxicity of ammonia and nitrite to Siamese fighting fish (Betta splendens). BMC Zool. 2023 Nov 2;8(1):25. doi: 10.1186/s40850-023-00188-3. PMID: 37915084; PMCID: PMC10621081.
Abstract
The acute toxicity and sublethal effects of ammonia and nitrite on the air-beathing Siamese fighting fish, betta (
Betta splendens) was studied for 96 h. The LC50 (50% Lethal Concentration) for 96 h for adult bettas to ammonia-N and nitrite-N was 123.4 mM (1.7 g/L, 95% confidence limits: 114.7–130.0 mM) and 24.6 mM (343.6 mg/L, 95% confidence limits: 22.7–26.4 mM) respectively. Exposure to 90 mM ammonia did not affect ammonia and urea excretion rates in bettas. There was no significant difference in values between control and ammonia-loaded (90 mM ammonia) individuals in either brain or liver activities of glutamine synthase, while plasma ammonia levels slightly increased. It appears unlikely that ammonia was converted to urea or amino acids for detoxification. Sublethal nitrite (24.6 mM nitrite) affected plasma nitrite, methemoglobin and hemoglobin. Plasma nitrite values remained much lower than ambient concentrations. Betta has a labyrinth organ and can breathe air. Bettas may temporarily reduce the entry of ammonia and nitrite into the body by increasing the rate of air respiration and reducing the contribution of the gill epithelium, which is highly permeable to these nitrogenous pollutants.
Full paper here:
https://pmc.ncbi.nlm.nih.gov/articles/PMC10621081/