At 2k words if you begin immersion you can pick out words in sentences. You will have to look up a word in almost every sentence and often multiple words per sentence.
At 4k words you will generally be able to read simple sentences with context, but will still be looking up a word in almost every sentence.
At 6k words you will be able to read most simple sentences and with most lower level books (like Kuma Kuma Kuma Bear for example) you will only have to look up a few words per page.
At 8k words you will be able to read most popular fiction aimed at the junior high and below crowd, but will still need to look up a few words per page.
At 10k words you will be able to read most popular fiction, but will still need to look up a decent number of words per page.
Note that this is my personal guideline and that each level will depend on where you learned the words from and what you are attempting to read. The answer to when you should start immersion is mostly dependent on how frustrated you get with looking words up. Some people start at 2k and have no problem looking up every other word. Personally I say wait until the 4-6k range, but you can always try earlier and if it’s too frustrating just put it off till later.