I can't really comment on the first time I attempted transition, it was so long ago now that I can't remember my frame of mind when going out. I think I was most afraid of being stopped by the cops while driving since my licence and rego were in my male name. Other than that I think I was OK.
Despite the twenty plus years gap I was able to retain that mostly-confident mind set when starting out again. My very first trip out the front door was a quick trip in the dark to take out the trash which remarkably prepped me more than I expected. The very next day I went to see my counsellor at the Gender Center - walked to the train station via the large mall near where I live, caught a train, walked to the center, then afterwards caught the train into the city and walked to work! Got changed at work. It was an absolute buzz.
I had a few more trips out to various things over the next couple of weeks, each one a bit more demanding than the other. The most testing was going to an art show being put on by a friend, it was in a very crowded place and I was so freaked I almost didn't go in... pushed through my fear and had a fantastic evening which included dinner afterwards with a number of other women at the show. It was shortly after that moment that I decided I was probably more ready than I realised.
So yeah, I wouldn't say I wasn't afraid in those earlier moments, but not letting the fear own me, making sure I was safe and making sure I had a reasonable escape strategy if needs be really helped me through.