No, it is not the right option, and while some sentences may begin with though, your "sentence" is not a sentence!
It would be a sentence if it were worded as follows (it includes corrected spelling in brackets):
"Though she spent most of her time [sitting on] the wooden steps that led to the beach, gazing vacantly at the blue ocean, she gradually came out of her shell and began talking to us in very short sentences."
If you want to start a sentence with though, make sure you complete the thought you started with though.
"Though I was not inclined initially to attend the party, I decided at the last minute to go, if only to get a free meal."
"Though reluctant, I acceded to her request."
"Though retired, he kept busy with his hobbies."
This kind of sentence structure works well when you are contrasting two different ideas side-by-side. As you can tell from my examples, after the "though" section of the sentence it is good to insert a personal pronoun. The following sentence, for example, would not be correct:
"Though retired, his hobbies kept him busy."
This sentence gives the impression the man's hobbies retired, and not the man himself!