I think that there are 2 kinds of instagrammers:
-The first one operates on an high number of account and can't handle them manually. He needs bot activity to drive traffic to his link in bio and make affiliate commissions. In this case you absolutely need bots and all you need is clicks. You don't need a great growth or engagement. You just work on the quantity and on the bot settings to optimise the automation.
-The second one works on a single account or on a few account. His goal is not to make affiliate commissions but to create an audience to make lead generation, sell his own digital product, start an e-commerce, sell shootout, or whatever his goal is. In this case I think that using bot is the worst thing you could do. This is a long term game and bot kill your engagement and your growth in the long term.
You should keep your activity high and network with other people in your niche. Personally, I think at the beginning you should invest something to get leverage.
Both the strategies work really well if you know what to do. I think there is a good way to do the first method and a good way to do the second.
From my experience botting is never a good idea if you are working on quality and not on quantity.
And about how to grow so quickly in a short period of time. In most cases you need big pages or you need to invest.
I can do that, but I perfectly understand that if I didn't have my pages I wouldn't be able to do that. And I invested at the beginning to get where I am now.
My personal advice is networking with other serious and focused people.