I believe your friend either misunderstood or was given the wrong advice. Based on being Cuban, he will apply to adjust to permanent resident status one year after CBP paroled him into the United States. That is the green card application. Once he applies for the green card and work permit, he will receive I-485/I-765 receipts as soon as USCIS cashes his filing fees. Those receipts will make him an adjustment of status applicant. After receiving the receipts, USCIS will schedule him for biometrics. He will later receive his work permit in the mail.
Once after your friend applies for adjustment under the Cuban Adjustment Act he will get some receipts from immigration. That will serve as evidence of his status in the United States as an adjustment applicant until he receives his work permit.