Is it possible to develop insomnia within the first week of using Prozac?

Hi, Anon!
"Very common (10% or more of users): Insomnia (up to 33%), anxiety (up to 15%), nervousness (up to 14%)"
"Side effects have been reported to be generally mild and transient. They are most common during the first 2 weeks of treatment and decrease in intensity and frequency with continued treatment. They generally do not lead to treatment cessation."
Best regards, Wildcat

Yes, this is a common side effect so it's typically taken in the morning. If you're taking it at night definitely consider switching to the AM. See how it goes & speak with your MD about all of your side effects. Good luck!