It is hard to say whether there are too many 'at first's without knowing how long the story is and how frequently this phrase appears with respect to other phrases. On the other hand, the phrase itself has an impact on your writing that you may or may not want to avoid.
When you use at first, you pull the reader out of the immediate narrative to reflect on a sequence of events. You are doing this because you are numbering the things that happened, so to the reader, none of it can be happening right now. You might want to do this—if you are filling in back story, for instance—but if that's not your intent, you'll need to take a different approach.
For example, if I want to tell you about a girl I met last night, I use the at first version:
We were reminiscing about our past relationships, and Mrs. Kondo asked Akiko about her first love (she'd only had two in her life: me and her high school sweetheart). At first Akiko had been a reluctant to answer, however, as the cocktails flowed, she became more and more enthusiastic.
If I want the reader to sit invisibly next to me while this is actually happening, then the form needs to be different, and probably would be expanded with dialog.
"I remember my first kiss," Mrs. Kondo smiled faintly. "Under the cherry blossoms at my parent's house. What about you, Akiko?"
Akiko avoided her gaze and slipped a second glass off the nearest tray. I watched her take the first drink, a little deeper than usual, before she squared her shoulders slightly. She drew in a breath to reply, then caught my eye and faltered. "It wasn't quite that romantic," she smiled graciously. "Not like when you were young."
Mrs. Kondo patted her shoulder and prattled on, Akiko drinking faster and faster as the night progressed. The alcohol and boredom loosened her lips and as I left, she was filling Mrs. Kondo in on the details of the dance where I told her I loved her for the first time.
That's a lengthy example, but I mean to demonstrate how you can show the kind of progress that you would otherwise tell with an 'at first' style statement.