No. Once you apply for and receive certain NIH awards, you no longer qualify as a new investigator or an early-stage investigator (ESI). See the List of Smaller Grants and Awards you can get and still be considered new or ESI.
If your award type isn't on that list of exceptions, e.g., Research Project—Cooperative Agreements (U01), you lose your ESI or new investigator status when you get the award.