While it is NOT a rule, it is improper English. Many professors have agreed that reading papers with sentences that begin with "So..." says this student was not taught PROPER English. However, the sentence above is like poetry -and in poetry or descriptive writing, we NEED to heighten the characteristics of what we are talking about -the subject (the subject in the above sentence: 'the undergrowth'; the description: 'so dense'. In that sentence, with using 'so', it is fine...actually wonderful...pleasing to the reader (I knew how dense the undergrowth was before I knew that John spent five minutes in it..and I was able to visualize this better)
Go back to First grade for a moment and think about how you would talk to a five or six year old to excite them. Perhaps something like, "The oceanic habitat is home to millions of sea creatures-even sharks!" (I'm letting students know about the ocean -like the initial sentence let me know about the undergrowth -I, as would a five or six year old, would be intrigued.) Then I would say, "Oceans cover seventy-five percent of our Earth!" (Kids would think about how high of a number that is and be amazed-even more excited, and perhaps be able to visualize an imaginative sight of all of those fish and sharks covering MOST of the world! ....like in the initial sentence when I found out that John was lost in five minutes-because of how dense the overgrowth was.)
Now, if you're still with me, here are the best times to use the improper English 'so' at the beginning of a sentence.
-When writing poetry: "So lovely was the lavender lilacs, I could only breathe in a sweet smell."
-when making an impression on informational essay writing (THIS IS ONLY OKAY 1-2 TIMES) "So these colonies stood strong, just as our America has become."
-when giving speeches (also, see above) "So I say to all my family and friends, take my words and think of them when the sun stops shining so bright!"
***YOU don't need to know proper English to change the world. Writing comes from the heart -your thoughts, feelings; and you'd be surprised at how many published pieces look when they first arrive at a publishing company! Bottom line, if it's meant to be good, it will be...or eventually will be. So, that's all I got.