Dear Deborah Harrell:
Thank you for posting your question on History Hub.
Information about census records can be found on our website at https://www.archives.gov/research/genealogy/census/about. Many of these records have been digitized and are available through our partners. For additional information about accessing these records, you can visit our website. These records might assist you after Peter's arrival to the US.
If you know the point of entry into the US, passenger lists may be a source of additional information. You may wish to search Ancestry or FamilySearch for the passenger lists. There may be a fee for using Ancestry. Instead, please check for access at your local library as many library systems subscribe to these sites, making them free for their patrons.
You may wish to consult the FamilySearch German Online Genealogy Records Wiki. They have information about finding vital records such as birth certificates.
We hope this information assists you with your research!