In short just do it, or make a plan like I did. Only you can decide the right path.
Well I had a big process, well at least I thought it was. I had been living full time Reann socially for over two years closer to three when I decided I needed to be out. You can read my fun story about how I started to come out at work, at my Favourite coming out story and the story of me coming out to the Public Service Allience of Canada at Coming out to the local PSAC I came out to the Union of National Employes as well, but that was because I was having some other issues with some people who worked above me, that is not a fun story or one I feel safe sharing. I was off work for a while because of some work and family things. When I got back my new senior had mentioned something about her talking to a co-worker in a different department, and how it threw this other colleague for a loop about me being me. My senior suggested I write a letter to be sent out to all the people working in UNE 40040 so I searched the internet and found one that I used as a template, if I remembered where I found it I would link to it as I believe in giving credit where credit is due. I asked my senior if she could proof it before it was sent she agreed, so I sent it to her when she got back to me I was told that she was expecting one or two sentences maybe two paragraphs not a page. You can see it here Coming out trans to co-workers. I encourage you to use it as your template if that is the way that you choose to go. All of this happened over the course of close to a year.
If I where to need to do it again I would just rip the bandaid right off. I did it slow because that was the process I thought would work for me. As someone had told me I would lose my job and I would be unemployable if I where to “become” trans, I was scared and I wanted to move all of the parts slowly. If I moved through all off the parts slowly I would learn how each part may move independently giving me a broader sense of my transition, and giving me a foot to stand on if the threat was true and I needed to fight it.
I may also mention that; I am so far out that I cannot even see the closet anymore.