No. Travelers entering the United States with ESTA are generally allowed to stay for up to 90 days, and an ESTA stay extension is not normally permitted after arrival.
Also, travelers admitted with ESTA are generally not allowed to extend their stay or change to another status after entering the United States.
For that reason, if you plan to stay longer than 90 days, it is better to check the appropriate visa option before traveling.
If you have already entered with ESTA, the important step is to confirm your allowed period of stay and make sure your departure plans fit within that period.