When you file your weekly or bi-weekly benefit certification and claim you must truthfully answer few questions. You're asked if you worked and how much you earned. You must show your earnings even if you have not yet been paid. If your claim period includes partial weeks of work and earnings you'll generally be eligible for partial unemployment benefits. However for any weeks where you worked the entire week you will not receive any benefits.
There may be a gap with no income coming in. Unfortunately there's nothing that you can do about that. Some folks will claim an extra week of UI benefits to "tide themselves over" until their first paycheck arrives however the odds of getting caught out are virtually 100% since your wages are reported to the state and the state cross-references wage and UI benefit payments.
At the very least you'd be required to pay back the UI benefits that you fraudulently claimed. In serious cases of fraud you can even be prosecuted and most states treat unemployment benefit fraud as a crime regardless of the amount of money involved.