One of the jobs I'm at I was at for a little over one year when I came out.
I had told the person I met first and was closest to gauge a reaction. She had said it would feel weird for he to call me "Cal/aka preferred name" but that she's glad I was finding what I needed to be myself.
Telling my other co-workers came easily after telling the first one. We work retail and are a very small store. Right now we have only seven employees including myself.
Telling the store manager was just difficult because she tended to be unnecessarily vocal about her devout ties to Catholicism. I knew she couldn't actually say or do anything but still the concern was there. One day I get fed up with having to deal w/her using my birth name& female pronouns so we went in the back& I told her I am regarded as male everywhere but at work, that I would be starting to medically transition& that I ask that she refer to me by my preferred name& use male pronouns.
End of story

Like others I suggest you tell someone you trust at work first& then be sure to tell those in charge to avoid what someone else also said, those higher up finding out from regular co-workers.
Good luck, I hope it goes well.