Difference between 'time to index' and 'time to rank'

1. Through my experience with my own website and reading on BHW I know that majority of sites get indexed in a few days to ~ 2 weeks.
2. However, the time for the article to rank to its 'deserved' position seems to take around 2~4 months (when it starts seeing some proper organic traffic)

My question is - do backlinks ONLY affect the ranking, or does it also affect the time it takes to rank to its deserved position? Is there any other ways to reduce the time for item 2 above?

Anyone have any insights?

I don't think so, backlinks do help get you to a good position, but your right, you do have to wait for a while after "finishing" your site.
Nothing wrong with that, just work on another couple of projects in the mean time, and get those cooking.

Time To Index: Google takes about 1-7 days to Index your content, and one of the ways to do it is by posting your URL on the Google Search console.

Time To Rank: It basically depends on how you manage your SEO, once you have completed your SEO in a proper way then there is a chance that your content might rank Google Search Engine. There is not any specific time period of ranking, it completely depends on you that how you manage your SEO.

It depends. If a big site publishes a post it will rank almost instantly. If a small site publishes a new post it will take at least three weeks to rank well.

Time To Index: Google takes about a week to index your content.

Time To Rank: It totally depends on how you manage your SEO activities.