Shirleen, the expression "there was a time" refers more to a period of time in the past when things were different from today's. As you already point out, in your sentence, it sounds unnatural to English speakers. I think the right expression to start the sentence will depend a lot on the context of the text you are writing. You can say "There was once a little boy...", but are you going to focus your story on the boy, on the surgery? There are several options to chose from and you would like to select the expression which sounds better with the flow of your narrative

Personally, I use "once" as a general term, "on one occasion" for an example of something and "there was a time" for something that occurred but due to a change, the same kind of situation would be done differently. Examples: Once - Once, I accidentally left my phone on my co-worker's desk. On one occasion - My boss can be very moody! On one occasion I asked her if she wanted some cake and she snapped back at me, "What, you're trying to get me fat?" There was a time - I really love haunted houses, but there was a time when you would literally have to drag me into one!