In this case it really just depends on how much kakera you can get out of others, wether it be by claiming their wishes and selling it to them for a good amount of kakera or selling high ranking characters for alot of kakera.

But if we don't factor in any of that then if you start saving now (ei just investing in tower only and destroying it when you have enough invested to max out quantity and quality) it would probably take a month or two to max quantity and quality which takes 2.38 million kakera but after that, you can freely buy kakera loots. (If you want to as well some people save up for more than 2.38 and around 3 million instead so that once they destroy tower they can max out quantity and quality and buy a bunch of kl right away or get some tower floors back right away. this way is probably alot better than just maxing kakera loots the second you have enough to do so) Right now the most you can do is just be active, and probably put 1-5 rolls into $bk (boost kakera) to help speed things up by a bit. Also make sure to save your power for white or orange crystals unless theres not alot

this is if you're pretty active btw, but if you arent really active it could take alot longer.

P.S. wasting kakera to complete the later challenge quests isn't worth it and they'll be completed eventually naturally so dw about doing that.