If your computer was shipped with AppleCare's extended protection plan
purchased and activated on the computer, and the computer arrived
already, check your receipts including email receipts, for documentation.
You can also check to see if that AppleCare appears active through an
Online Service Assistant, by entering your products serial number.
Online Service Assistant:
https://selfsolve.apple.com/GetWarranty.do
The documentation accompanying the computer's purchase is used
for proof of purchase, and if/when AppleCare extended plan is added
to the original purchase, documentation (via email and perhaps later
via mail or to a valid street address) may also be sent. Apple Sales
support has a phone number, so you should discuss this with them.
The online service assistant page will require authentication to some
extent before it will show you anything; but there should be evidence
of the extended AppleCare plan, if it was enrolled after purchase, there
and the expiry date would be evidence, since the total time should be
indicative of the complementary first year of service, plus two years.
And a total of three years for both service and support on the product.
Purchases through the online store are quite easy to track, and the
validation of the AppleCare you opted to be active with the computer
should appear on your receipt from the online store; the email and
possibly some additional documentation. So, as suggested earlier,
contact Apple to see if you should be expecting paper documentation
and or any other AppleCare physical items sent to you. Perhaps not.
The link above should show a confirmation of an active AppleCare.
The duration should confirm if the automatic enrollment was done.
Good luck & happy computing! 🙂