Howdy, Edward! Thanks for bringing your question to the Disney Parks Moms Panel!
You can absolutely use your Annual Passport on the same day that you purchase it. You can
buy your Annual Passport online or at a ticket booth at the Disneyland Resort. If you purchase it online and select the eTicket option at check out, you will receive a voucher that you can take directly to the gates of either Disneyland Park or Disney California Adventure Park. Just keep in mind that you will have to visit a ticket booth sometime during the day of your first visit to pick up your Annual Passport card.
If you happen to purchase your Annual Passport on day that is
blocked out for that passport type, you are usually granted a one-time exception to enter the parks on that day, if capacity allows it. This means that if the parks are extremely busy that day, they may reach capacity and additional Guests won't be allowed to enter due to safety concerns. This doesn't happen very often, but just something to keep in mind.
I hope this helps clarify things for you. Enjoy using your Annual Passport all year long at the Disneyland Resort!
-Linda M.