The social security card has not been issued yet. Can I see a doctor in a different place?

No, the settlement procedures for people resettled in different places:

For the resettlement of staff from different places, the designated medical institution with the residence of 1-2 shall be designated by the unit to which it belongs, and it shall be reported to the medical insurance agency for the record;

The medical expenses incurred by the off-site staff in the outpatient department of the designated medical institution in their place of residence shall be paid in advance by themselves or their units. After the treatment, the unit holding the insured's diagnosis and medical records, effective bills, compound prescriptions and hospitalization expenses list shall settle the accounts with the social medical insurance agency on the specified date.