US visas do not have a start date, so the visa itself is valid from the moment it is issued. This doesn't help, however, because your admissibility in P-1 status also depends on the period of validity of the approved petition.
The relationship between the petition's validity and the beneficiary's admissibility may be found at 8 CFR 214.2(p)(12):
(12) Admission. A beneficiary may be admitted to the United States for the validity period of the petition, plus a period of up to 10 days before the validity period begins and 10 days after the validity period ends. The beneficiary may not work except during the validity period of the petition.
So you can enter up to 10 days before the petition's start date, but the regulation emphasizes that you may not work during those 10 days.
If you want to enter the US earlier than that, you would have to enter as a tourist, and then either leave the US and re-enter in P-1 status or apply for an in-country change of status. The latter option is not available to travelers using the visa waiver program, and the filing fee for the application form is $370.