Did Maria begin putting her hair up before she was sixteen?
No, even while she was still sixteen you can find pictures of her with her hair down (1913 Tercentenary photographs). She had certainly begun to style her hair on top of her head by 1914, as can be seen in the photographs during their last stay at Livadia and cruise in the Finish fjords.
Maria wasn't sixteen in 1913. She was only 14 then. I believe she did start to wear her hair up early as she was wearing it up in 1914 when she didn't turn sixteen yet.
Good lord, I thought she was born in 1897 but realized it was 1899 instead x__x. I thought she was Tatiana's age by mistake.
So to restate that answer, then yes, yes she did put her hair up before she was sixteen. Thank you Holly for proclaiming my error.
A request; does anyone have the photograph of Olga and Tatiana walking along the side of Peterhof Palace? I believe they're wearing long white dresses or coats and have their hair up...
This one?

Yes that's it!! I'm using it for an art project

Thank you immensely Sarushka!!
Thank you very much for your information!
I was just about to post that same photograph as Sarushka for NAOTMAA Fan.
Well thank you very much Ferah, it's the thought that counts!