You've asked the $1 million question, literally. If you crack the suggested riddle, your channel will fly high to dizzying heights!
We've had many discussion here over the last 9 months about it, you can look through my username and
@FamilyToyReview.
What I think it comes down to, is what I call shadowing. You pick a channel you want to be like, and shadow their videos. Not copy, but shadow closely.
You'll notice every time there is a new craze on Yt, starting with surprise eggs, then giant surprise eggs, then superheroes IRL, then bad babies (Toy Freaks), and dozens of other smaller sub-trends, as soon as the big channel (1M+) releases a video or 2, the smaller channels (100k-1M) jump on the bandwagon and shadow similar videos.
The algo, when looking for suggested placements, has many things to consider. It will place some of the videos off that same channel on there, it will place 'recommended for you' which are more tailored to the user's past habits, and suggested videos form other channel which it thinks are a good match. You have to make your videos that good match. So if you shadow match keywords, topics, and build some authority, you have a higher chance to jump on there.
When we started, I did this with Thomas and Step2. We got many suggested spots on 5k-50k channels (all related to those keywords), and that is a large part what drove our traffic and subs between 2k-10k subs.