I'm a nube... but here are my observation from practice. Without inoculation (natural LAB ferment), I've seen the most activity in the first week. I've also added high sugar components to my ferments so the LAB has plenty of food to go after. These have included sweet onion, carrot and red bells. The resulting pH has been about 3.0-3.3 every occasion after 3-4 week (7-10 days on the counter then into the fridge). Not having a food processor, I spilt the peppers in half, ferment, then run through the Vita Mix blender after fermentation has broken down the cell structure.
Intuitively, the faster the CO2 blanket forms and quicker the pH drops, the "safer" the ferment will be. So, in order to achieve this, helping the natural LAB with a spike of introduced LAB along with more sugar will get the process going faster and the pH lower. I plan to do this with future ferments even though "natural" has worked so far.
Having experience with wine making, natural yeast will ferment your grapes. However, inoculation with a specific strain of yeast gets the process going without the risk of less desirable yeasts doing their thing first. The increased control over the fermentation process increases the likelihood of a good, repeatable result.
I'd say "safe" is achieved within the first 10 days or so based on my experience (provided the LAB takes off and starts partying down on the available sugar).
Like wine, it's all about the aging process for flavor and complexity.