I will share that when I first started riding, almost 2 years ago, I had a heavy, clunky bike and walked up every single hill. Then I got a little hybrid that I rode for about 6 months and walked up about 1/2 the hills. A little over a year ago, I got my Trek 2.3. At first, I walked up just a few of the hills. This season, I have not walked up any hills, and I'm doing all the rides that I have been doing + a few more challenging.
I am 57 years old and trying desperately to lose 20 pounds. For 55 years of my life, I was more or less sedentary. So, have patience with yourself and envision yourself in +/- a year where you will ride up every hill!
And guess what? There are plenty of people out there that are too unfit to walk up 'dem hills
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"I never made "Who's Who"- but sure as hell I made "What's That??..."