When should an EB-5 applicant get their priority date?

It is the date received - you should not worry - this is common.

The priority date is set when USCIS receives the I-526 petition.

The priority date is issued when the immigrant petition, in this case the I-526, is approved, which will be the date of filing. With the receipt notice, the box for priority date is always empty as the PD cannot be conferred until the petitioner's case is approved. If the petition is ultimately denied, there is no priority date because there are no rights for the petitioner to be able to immigrate.

Her lawyer is correct. The priority date is the date the form I-526 was filed with USCIS, regardless if the date was stated in the receipt notice or not.

You should receive it when the application is initially processed, but China seems to be a special case as it is the only EB-5 country with waiting periods for visas.

For most immigration processes, the priority date is the date of filing the initial petition with USCIS, which should be noted on the receipt notice (form I-797).