Well, you didn't specify whether or not you are MTF or FTM, so I can tell you that, as a FTM, the changes are difficult to hide once your voice starts cracking! I was around a month in when I would wake up wondering if I would sound female or male. It got so that every morning it was a game of "What Gender Do I Sound Like Today?"
Other changes that came around pretty quickly were, facial and body hair. I ended up with a slight mustache, my arms became hairy and my sideburns, which I always let grow, started creeping down my face to form the beginnings of a beard. Boy, was I happy when that happened!
There were other changes, of course, such as my facial shape. I still have a (genetically) round face, but I'm happy that some of the fat has been redistributed. Unfortunately, I now have a bit more belly fat than before! My hips are thinner, and I also lost fat from my thighs. My upper arms and shoulders are also more muscular, which gave me the courage to finally go without wearing my hoodie, which I used to wear to hide my body shape. Now, I have a tendency to only wear it when I'm cold. I've always been the "jeans and graphic t-shirts-type," so my going without my hoodie showed off my upper arms and shoulders more. Now that skinny jeans have made a comeback, I wear those as well. My partner says I definitely have a more masculine body shape, despite still having some hips.
So to answer your question, I think I could have hidden my transitioning for maybe...three weeks to a month and a half if I spoke. If I didn't speak, I think I could have hidden myself for around two and a half to three months before my mustache really started growing in. Its still sparse, but its definitely there.
Are you FTM or MTF?
Ryuichi